More on Entrepreneurship/Creators

Esteban
2 years ago
The Berkus Startup Valuation Method: What Is It?
What Is That?
Berkus is a pre-revenue valuation method based exclusively on qualitative criteria, like Scorecard.
Few firms match their financial estimates, especially in the early stages, so valuation methodologies like the Berkus method are a good way to establish a valuation when the economic measures are not reliable.
How does it work?
This technique evaluates five key success factors.
Fundamental principle
Technology
Execution
Strategic alliances in its primary market
Production, followed by sales
The Berkus technique values the business idea and four success factors. As seen in the matrix below, each of these dimensions poses a danger to the startup's success.
It assigns $0-$500,000 to each of these beginning regions. This approach enables a maximum $2.5M pre-money valuation.
This approach relies significantly on geography and uses the US as a baseline, as it differs in every country in Europe.
A set of standards for analyzing each dimension individually
Fundamental principle (or strength of the idea)
Ideas are worthless; execution matters. Most of us can relate to seeing a new business open in our area or a startup get funded and thinking, "I had this concept years ago!" Someone did it.
The concept remains. To assess the idea's viability, we must consider several criteria.
The concept's exclusivity It is necessary to protect a product or service's concept using patents and copyrights. Additionally, it must be capable of generating large profits.
Planned growth and growth that goes in a specific direction have a lot of potential, therefore incorporating them into a business is really advantageous.
The ability of a concept to grow A venture's ability to generate scalable revenue is a key factor in its emergence and continuation. A startup needs a scalable idea in order to compete successfully in the market.
The attraction of a business idea to a broad spectrum of people is significantly influenced by the current socio-political climate. Thus, the requirement for the assumption of conformity.
Concept Validation Ideas must go through rigorous testing with a variety of audiences in order to lower risk during the implementation phase.
Technology (Prototype)
This aspect reduces startup's technological risk. How good is the startup prototype when facing cyber threats, GDPR compliance (in Europe), tech stack replication difficulty, etc.?
Execution
Check the management team's efficacy. A potential angel investor must verify the founders' experience and track record with previous ventures. Good leadership is needed to chart a ship's course.
Strategic alliances in its primary market
Existing and new relationships will play a vital role in the development of both B2B and B2C startups. What are the startup's synergies? potential ones?
Production, followed by sales (product rollout)
Startup success depends on its manufacturing and product rollout. It depends on the overall addressable market, the startup's ability to market and sell their product, and their capacity to provide consistent, high-quality support.
Example
We're now founders of EyeCaramba, a machine vision-assisted streaming platform. My imagination always goes to poor puns when naming a startup.
Since we're first-time founders and the Berkus technique depends exclusively on qualitative methods and the evaluator's skill, we ask our angel-investor acquaintance for a pre-money appraisal of EyeCaramba.
Our friend offers us the following table:
Because we're first-time founders, our pal lowered our Execution score. He knows the idea's value and that the gaming industry is red-hot, with worse startup ideas getting funded, therefore he gave the Basic value the highest value (idea).
EyeCaramba's pre-money valuation is $400,000 + $250,000 + $75,000 + $275,000 + $164,000 (1.16M). Good.
References
https://medium.com/humble-ventures/how-angel-investors-value-pre-revenue-startups-part-iii-8271405f0774#:~:text=pre%2Drevenue%20startups.-,Berkus%20Method,potential%20of%20the%20idea%20itself.%E2%80%9D
https://eqvista.com/berkus-valuation-method-for-startups/
https://www.venionaire.com/early-stage-startup-valuation-part-2-the-berkus-method/

Woo
2 years ago
How To Launch A Business Without Any Risk
> Say Hello To The Lean-Hedge Model
People think starting a business requires significant debt and investment. Like Shark Tank, you need a world-changing idea. I'm not saying to avoid investors or brilliant ideas.
Investing is essential to build a genuinely profitable company. Think Apple or Starbucks.
Entrepreneurship is risky because many people go bankrupt from debt. As starters, we shouldn't do it. Instead, use lean-hedge.
Simply defined, you construct a cash-flow business to hedge against long-term investment-heavy business expenses.
What the “fx!$rench-toast” is the lean-hedge model?
When you start a business, your money should move down, down, down, then up when it becomes profitable.
Many people don't survive the business's initial losses and debt. What if, we created a cash-flow business BEFORE we started our Starbucks to hedge against its initial expenses?
Lean-hedge has two sections. Start a cash-flow business. A cash-flow business takes minimal investment and usually involves sweat and time.
Let’s take a look at some examples:
A Translation company
Personal portfolio website (you make a site then you do cold e-mail marketing)
FREELANCE (UpWork, Fiverr).
Educational business.
Infomarketing. (You design a knowledge-based product. You sell the info).
Online fitness/diet/health coaching ($50-$300/month, calls, training plan)
Amazon e-book publishing. (Medium writers do this)
YouTube, cash-flow channel
A web development agency (I'm a dev, but if you're not, a graphic design agency, etc.) (Sell your time.)
Digital Marketing
Online paralegal (A million lawyers work in the U.S).
Some dropshipping (Organic Tik Tok dropshipping, where you create content to drive traffic to your shopify store instead of spend money on ads).
(Disclaimer: My first two cash-flow enterprises, which were language teaching, failed terribly. My translation firm is now booming because B2B e-mail marketing is easy.)
Crossover occurs. Your long-term business starts earning more money than your cash flow business.
My cash-flow business (freelancing, translation) makes $7k+/month.
I’ve decided to start a slightly more investment-heavy digital marketing agency
Here are the anticipated business's time- and money-intensive investments:
($$$) Top Front-End designer's Figma/UI-UX design (in negotiation)
(Time): A little copywriting (I will do this myself)
($$) Creating an animated webpage with HTML (in negotiation)
Backend Development (Duration) (I'll carry out this myself using Laravel.)
Logo Design ($$)
Logo Intro Video for $
Video Intro (I’ll edit this myself with Premiere Pro)
etc.
Then evaluate product, place, price, and promotion. Consider promotion and pricing.
The lean-hedge model's point is:
Don't gamble. Avoid debt. First create a cash-flow project, then grow it steadily.
Check read my previous posts on “Nightmare Mode” (which teaches you how to make work as interesting as video games) and Why most people can't escape a 9-5 to learn how to develop a cash-flow business.

Bernard Bado
2 years ago
Build This Before Someone Else Does!
Do you want to build and launch your own software company? To do this, all you need is a product that solves a problem.
Coming up with profitable ideas is not that easy. But you’re in luck because you got me!
I’ll give you the idea for free. All you need to do is execute it properly.
If you’re ready, let’s jump right into it! Starting with the problem.
Problem
Youtube has many creators. Every day, they think of new ways to entertain or inform us.
They work hard to make videos. Many of their efforts go to waste. They limit their revenue and reach.
Solution
Content repurposing solves this problem.
One video can become several TikToks. Creating YouTube videos from a podcast episode.
Or, one video might become a blog entry.
By turning videos into blog entries, Youtubers may develop evergreen SEO content, attract a new audience, and reach a non-YouTube audience.
Many YouTube creators want this easy feature.
Let's build it!
Implementation
We identified the problem, and we have a solution. All that’s left to do is see how it can be done.
Monitoring new video uploads
First, watch when a friend uploads a new video. Everything should happen automatically without user input.
YouTube Webhooks make this easy. Our server listens for YouTube Webhook notifications.
After publishing a new video, we create a conversion job.
Creating a Blog Post from a Video
Next, turn a video into a blog article.
To convert, we must extract the video's audio (which can be achieved by using FFmpeg on the server).
Once we have the audio channel, we can use speech-to-text.
Services can accomplish this easily.
Speech-to-text on Google
Google Translate
Deepgram
Deepgram's affordability and integration make it my pick.
After conversion, the blog post needs formatting, error checking, and proofreading.
After this, a new blog post will appear in our web app's dashboard.
Completing a blog post
After conversion, users must examine and amend their blog posts.
Our application dashboard would handle all of this. It's a dashboard-style software where users can:
Link their Youtube account
Check out the converted videos in the future.
View the conversions that are ongoing.
Edit and format converted blog articles.
It's a web-based app.
It doesn't matter how it's made but I'd choose Next.js.
Next.js is a React front-end standard. Vercel serverless functions could conduct the conversions.
This would let me host the software for free and reduce server expenditures.
Taking It One Step Further
SaaS in a nutshell. Future improvements include integrating with WordPress or Ghost.
Our app users could then publish blog posts. Streamlining the procedure.
MVPs don't need this functionality.
Final Thoughts
Repurposing content helps you post more often, reach more people, and develop faster.
Many agencies charge a fortune for this service. Handmade means pricey.
Content creators will go crazy if you automate and cheaply solve this problem.
Just execute this idea!
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Looi Qin En
2 years ago
I polled 52 product managers to find out what qualities make a great Product Manager
Great technology opens up an universe of possibilities.
Need a friend? WhatsApp, Telegram, Slack, etc.
Traveling? AirBnB, Expedia, Google Flights, etc.
Money transfer? Use digital banking, e-wallet, or crypto applications
Products inspire us. How do we become great?
I asked product managers in my network:
What does it take to be a great product manager?
52 product managers from 40+ prominent IT businesses in Southeast Asia responded passionately. Many of the PMs I've worked with have built fantastic products, from unicorns (Lazada, Tokopedia, Ovo) to incumbents (Google, PayPal, Experian, WarnerMedia) to growing (etaily, Nium, Shipper).
TL;DR:
Soft talents are more important than hard skills. Technical expertise was hardly ever stressed by product managers, and empathy was mentioned more than ten times. Janani from Xendit expertly recorded the moment. A superb PM must comprehend that their empathy for the feelings of their users must surpass all logic and data.
Constant attention to the needs of the user. Many people concur that the closer a PM gets to their customer/user, the more likely it is that the conclusion will be better. There were almost 30 references to customers and users. Focusing on customers has the advantage because it is hard to overshoot, as Rajesh from Lazada puts it best.
Setting priorities is invaluable. Prioritization is essential because there are so many problems that a PM must deal with every day. My favorite quotation on this is from Rakuten user Yee Jie. Viki, A competent product manager extinguishes fires. A good product manager lets things burn and then prioritizes.
This summary isn't enough to capture what excellent PMs claim it requires. Read below!
What qualities make a successful product manager?
Themed quotes are alphabetized by author.
Embrace your user/customer
Aeriel Dela Paz, Rainmaking Venture Architect, ex-GCash Product Head
Great PMs know what customers need even when they don’t say it directly. It’s about reading between the lines and going through the numbers to address that need.
Anders Nordahl, OrkestraSCS's Product Manager
Understanding the vision of your customer is as important as to get the customer to buy your vision
Angel Mendoza, MetaverseGo's Product Head
Most people think that to be a great product manager, you must have technical know-how. It’s textbook and I do think it is helpful to some extent, but for me the secret sauce is EMPATHY — the ability to see and feel things from someone else’s perspective. You can’t create a solution without deeply understanding the problem.
Senior Product Manager, Tokopedia
Focus on delivering value and helping people (consumer as well as colleague) and everything else will follow
Darren Lau, Deloitte Digital's Head of Customer Experience
Start with the users, and work backwards. Don’t have a solution looking for a problem
Darryl Tan, Grab Product Manager
I would say that a great product manager is able to identify the crucial problems to solve through strong user empathy and synthesis of insights
Diego Perdana, Kitalulus Senior Product Manager
I think to be a great product manager you need to be obsessed with customer problems and most important is solve the right problem with the right solution
Senior Product Manager, AirAsia
Lot of common sense + Customer Obsession. The most important role of a Product manager is to bring clarity of a solution. Your product is good if it solves customer problems. Your product is great if it solves an eco-system problem and disrupts the business in a positive way.
Edward Xie, Mastercard Managing Consultant, ex-Shopee Product Manager
Perfect your product, but be prepared to compromise for right users
AVP Product, Shipper
For me, a great product manager need to be rational enough to find the business opportunities while obsessing the customers.
Janani Gopalakrishnan is a senior product manager of a stealth firm.
While as a good PM it’s important to be data-driven, to be a great PM one needs to understand that their empathy for their users’ emotions must exceed all logic and data. Great PMs also make these product discussions thrive within the team by intently listening to all the members thoughts and influence the team’s skin in the game positively.
Director, Product Management, Indeed
Great product managers put their users first. They discover problems that matter most to their users and inspire their team to find creative solutions.
Grab's Senior Product Manager Lakshay Kalra
Product management is all about finding and solving most important user problems
Quipper's Mega Puji Saraswati
First of all, always remember the value of “user first” to solve what user really needs (the main problem) for guidance to arrange the task priority and develop new ideas. Second, ownership. Treat the product as your “2nd baby”, and the team as your “2nd family”. Third, maintain a good communication, both horizontally and vertically. But on top of those, always remember to have a work — life balance, and know exactly the priority in life :)
Senior Product Manager, Prosa.AI Miswanto Miswanto
A great Product Manager is someone who can be the link between customer needs with the readiness and flexibility of the team. So that it can provide, build, and produce a product that is useful and helps the community to carry out their daily activities. And He/She can improve product quality ongoing basis or continuous to help provide solutions for users or our customer.
Lead Product Manager, Tokopedia, Oriza Wahyu Utami
Be a great listener, be curious and be determined. every great product manager have the ability to listen the pain points and understand the problems, they are always curious on the users feedback, and they also very determined to look for the solutions that benefited users and the business.
99 Group CPO Rajesh Sangati
The advantage of focusing on customers: it’s impossible to overshoot
Ray Jang, founder of Scenius, formerly of ByteDance
The difference between good and great product managers is that great product managers are willing to go the unsexy and unglamorous extra mile by rolling up their sleeves and ironing out all minutiae details of the product such that when the user uses the product, they can’t help but say “This was made for me.”
BCG Digital Ventures' Sid Narayanan
Great product managers ensure that what gets built and shipped is at the intersection of what creates value for the customer and for the business that’s building the product…often times, especially in today’s highly liquid funding environment, the unit economics, aka ensuring that what gets shipped creates value for the business and is sustainable, gets overlooked
Stephanie Brownlee, BCG Digital Ventures Product Manager
There is software in the world that does more harm than good to people and society. Great Product Managers build products that solve problems not create problems
Experiment constantly
Delivery Hero's Abhishek Muralidharan
Embracing your failure is the key to become a great Product Manager
DeliveryHero's Anuraag Burman
Product Managers should be thick skinned to deal with criticism and the stomach to take risk and face failures.
DataSpark Product Head Apurva Lawale
Great product managers enjoy the creative process with their team to deliver intuitive user experiences to benefit users.
Dexter Zhuang, Xendit Product Manager
The key to creating winning products is building what customers want as quickly as you can — testing and learning along the way.
PayPal's Jay Ko
To me, great product managers always remain relentlessly curious. They are empathetic leaders and problem solvers that glean customer insights into building impactful products
Home Credit Philippines' Jedd Flores
Great Product Managers are the best dreamers; they think of what can be possible for the customers, for the company and the positive impact that it will have in the industry that they’re part of
Set priorities first, foremost, foremost.
HBO Go Product Manager Akshay Ishwar
Good product managers strive to balance the signal to noise ratio, Great product managers know when to turn the dials for each up exactly
Zuellig Pharma's Guojie Su
Have the courage to say no. Managing egos and request is never easy and rejecting them makes it harder but necessary to deliver the best value for the customers.
Ninja Van's John Prawira
(1) PMs should be able to ruthlessly prioritize. In order to be effective, PMs should anchor their product development process with their north stars (success metrics) and always communicate with a purpose. (2) User-first when validating assumptions. PMs should validate assumptions early and often to manage risk when leading initiatives with a focus on generating the highest impact to solving a particular user pain-point. We can’t expect a product/feature launch to be perfect (there might be bugs or we might not achieve our success metric — which is where iteration comes in), but we should try our best to optimize on user-experience earlier on.
Nium Product Manager Keika Sugiyama
I’d say a great PM holds the ability to balance ruthlessness and empathy at the same time. It’s easier said than done for sure!
ShopBack product manager Li Cai
Great product managers are like great Directors of movies. They do not create great products/movies by themselves. They deliver it by Defining, Prioritising, Energising the team to deliver what customers love.
Quincus' Michael Lim
A great product manager, keeps a pulse on the company’s big picture, identifies key problems, and discerns its rightful prioritization, is able to switch between the macro perspective to micro specifics, and communicates concisely with humility that influences naturally for execution
Mathieu François-Barseghian, SVP, Citi Ventures
“You ship your org chart”. This is Conway’s Law short version (1967!): the fundamental socio-technical driver behind innovation successes (Netflix) and failures (your typical bank). The hype behind micro-services is just another reflection of Conway’s Law
Mastercard's Regional Product Manager Nikhil Moorthy
A great PM should always look to build products which are scalable & viable , always keep the end consumer journey in mind. Keeping things simple & having a MVP based approach helps roll out products faster. One has to test & learn & then accordingly enhance / adapt, these are key to success
Rendy Andi, Tokopedia Product Manager
Articulate a clear vision and the path to get there, Create a process that delivers the best results and Be serious about customers.
Senior Product Manager, DANA Indonesia
Own the problem, not the solution — Great PMs are outstanding problem preventers. Great PMs are discerning about which problems to prevent, which problems to solve, and which problems not to solve
Tat Leong Seah, LionsBot International Senior UX Engineer, ex-ViSenze Product Manager
Prioritize outcomes for your users, not outputs of your system” or more succinctly “be agile in delivering value; not features”
Senior Product Manager, Rakuten Viki
A good product manager puts out fires. A great product manager lets fires burn and prioritize from there
acquire fundamental soft skills
Oracle NetSuite's Astrid April Dominguez
Personally, i believe that it takes grit, empathy, and optimistic mindset to become a great PM
Ovo Lead Product Manager Boy Al Idrus
Contrary to popular beliefs, being a great product manager doesn’t have anything to do with technicals, it sure plays a part but most important weapons are: understanding pain points of users, project management, sympathy in leadership and business critical skills; these 4 aspects would definitely help you to become a great product manager.
PwC Product Manager Eric Koh
Product managers need to be courageous to be successful. Courage is required to dive deep, solving big problems at its root and also to think far and dream big to achieve bold visions for your product
Ninja Van's Product Director
In my opinion the two most important ingredients to become a successful product manager is: 1. Strong critical thinking 2. Strong passion for the work. As product managers, we typically need to solve very complex problems where the answers are often very ambiguous. The work is tough and at times can be really frustrating. The 2 ingredients I mentioned earlier will be critical towards helping you to slowly discover the solution that may become a game changer.
PayPal's Lead Product Manager
A great PM has an eye of a designer, the brain of an engineer and the tongue of a diplomat
Product Manager Irene Chan
A great Product Manager is able to think like a CEO of the company. Visionary with Agile Execution in mind
Isabella Yamin, Rakuten Viki Product Manager
There is no one model of being a great product person but what I’ve observed from people I’ve had the privilege working with is an overflowing passion for the user problem, sprinkled with a knack for data and negotiation
Google product manager Jachin Cheng
Great product managers start with abundant intellectual curiosity and grow into a classic T-shape. Horizontally: generalists who range widely, communicate fluidly and collaborate easily cross-functionally, connect unexpected dots, and have the pulse both internally and externally across users, stakeholders, and ecosystem players. Vertically: deep product craftsmanship comes from connecting relentless user obsession with storytelling, business strategy with detailed features and execution, inspiring leadership with risk mitigation, and applying the most relevant tools to solving the right problems.
Jene Lim, Experian's Product Manager
3 Cs and 3 Rs. Critical thinking , Customer empathy, Creativity. Resourcefulness, Resilience, Results orientation.
Nirenj George, Envision Digital's Security Product Manager
A great product manager is someone who can lead, collaborate and influence different stakeholders around the product vision, and should be able to execute the product strategy based on customer insights, as well as take ownership of the product roadmap to create a greater impact on customers.
Grab's Lead Product Manager
Product Management is a multi-dimensional role that looks very different across each product team so each product manager has different challenges to deal with but what I have found common among great product managers is ability to create leverage through their efforts to drive outsized impacts for their products. This leverage is built using data with intuition, building consensus with stakeholders, empowering their teams and focussed efforts on needle moving work.
NCS Product Manager Umar Masagos
To be a great product manager, one must master both the science and art of Product Management. On one hand, you need have a strong understanding of the tools, metrics and data you need to drive your product. On the other hand, you need an in-depth understanding of your organization, your target market and target users, which is often the more challenging aspect to master.
M1 product manager Wei Jiao Keong
A great product manager is multi-faceted. First, you need to have the ability to see the bigger picture, yet have a keen eye for detail. Secondly, you are empathetic and is able to deliver products with exceptional user experience while being analytical enough to achieve business outcomes. Lastly, you are highly resourceful and independent yet comfortable working cross-functionally.
Yudha Utomo, ex-Senior Product Manager, Tokopedia
A great Product Manager is essentially an effective note-taker. In order to achieve the product goals, It is PM’s job to ensure objective has been clearly conveyed, efforts are assessed, and tasks are properly tracked and managed. PM can do this by having top-notch documentation skills.

Vitalik
3 years ago
An approximate introduction to how zk-SNARKs are possible (part 2)
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3

Cory Doctorow
2 years ago
The downfall of the Big Four accounting companies is just one (more) controversy away.
Economic mutual destruction.
Multibillion-dollar corporations never bothered with an independent audit, and they all lied about their balance sheets.
It's easy to forget that the Big Four accounting firms are lousy fraud enablers. Just because they sign off on your books doesn't mean you're not a hoax waiting to erupt.
This is *crazy* Capitalism depends on independent auditors. Rich folks need to know their financial advisers aren't lying. Rich folks usually succeed.
No accounting. EY, KPMG, PWC, and Deloitte make more money consulting firms than signing off on their accounts.
The Big Four sign off on phony books because failing to make friends with unscrupulous corporations may cost them consulting contracts.
The Big Four are the only firms big enough to oversee bankruptcy when they sign off on fraudulent books, as they did for Carillion in 2018. All four profited from Carillion's bankruptcy.
The Big Four are corrupt without any consequences for misconduct. Who can forget when KPMG's top management was fined millions for helping auditors cheat on ethics exams?
Consulting and auditing conflict. Consultants help a firm cover its evil activities, such as tax fraud or wage theft, whereas auditors add clarity to a company's finances. The Big Four make more money from cooking books than from uncooking them, thus they are constantly embroiled in scandals.
If a major scandal breaks, it may bring down the entire sector and substantial parts of the economy. Jim Peterson explains system risk for The Dig.
The Big Four are voluntary private partnerships where accountants invest their time, reputations, and money. If a controversy threatens the business, partners who depart may avoid scandal and financial disaster.
When disaster looms, each partner should bolt for the door, even if a disciplined stay-and-hold posture could weather the storm. This happened to Arthur Andersen during Enron's collapse, and a 2006 EU report recognized the risk to other corporations.
Each partner at a huge firm knows how much dirty laundry they've buried in the company's garden, and they have well-founded suspicions about what other partners have buried, too. When someone digs, everyone runs.
If a firm confronts substantial litigation damages or enforcement penalties, it could trigger the collapse of one of the Big Four. That would be bad news for the firm's clients, who would have trouble finding another big auditor.
Most of the world's auditing capacity is concentrated in four enormous, brittle, opaque, compromised organizations. If one of them goes bankrupt, the other three won't be able to take on its clients.
Peterson: Another collapse would strand many of the world's large public businesses, leaving them unable to obtain audit views for their securities listings and regulatory compliance.
Count Down: The Past, Present, and Uncertain Future of the Big Four Accounting Firms is in its second edition.
https://www.emerald.com/insight/publication/doi/10.1108/9781787147003