I am very excited to announce that my Cryptics book is now available in U.S and many other countries on Amazon.

This is a perfect holiday gift for students, life-long learners, professionals, entrepreneurs and anyone interested in getting introduced to amazing math and crypto concepts in a fun way.

What is Cryptics ?

Cryptics is a hard science fiction novel and a technological thriller aimed at introducing some of the most amazing concepts of cryptography, blockchain, zero-knowledge proofs, artificial intelligence and mathematics in a fun, exciting and a memorable way.

It is a story of five middle school students, who meet at a talk given by Dr. Shiva Kintali, a billionaire mathematician and a technologist. Doc brings their attention to a puzzle, whose solution is worth $10 Billion. The students compete with some of the best cryptographers, cypherpunks, mathematicians, coders and hackers of this generation. In the largest global treasure hunt ever. In the history of humankind.

Amazon link

It is free for everyone. My main goal is to educate everyone using bite-sized links, in less than 10 minutes.

Subscribe using this substack link: shivakintali.substack.com

Here is the First post and the Second post.

Here is my next puzzle:

Let and and .

Let and and .

Also,

All the above variables are positive integers and and and

Prove or disprove the following claim:

Claim: There exists a rational number such that and are rational numbers.

If you want to take small baby steps towards a proof, start with the following special cases:

Special case 1: and

Special case 2: and and

Quick homework problem: Prove the Special case 2 using a proof of my previous puzzle.

Have fun solving.

Some mathematician has said pleasure lies not in discovering truth, but in seeking it

Prove or disprove the following statement:

• Claim: Let be positive integers such that and . Given two rational numbers , there exist positive integers such that and and is a perfect square.
• If the above statement is true, show an example of , expressed in terms of .
• If the above statement is false, construct a counterexample.

Leave your solutions in the comments. Have fun solving it.

• Let P=(v1, v2, v3, v4) be a simple polygon drawn on a plane.
• The co-ordinates of the vertices v1, v2, v3, v4 are all rational numbers.
• The lengths of the edges (v1, v2), (v2, v3), (v3, v4) and (v4, v1) are all integers.
• The distance between v1 and v3 is an integer.

Conjecture 1: There exists a point x with rational coordinates inside P such that the euclidean distances between the pairs (x, v1), (x, v2), (x, v3), (x, v4) are all rational numbers.

Conjecture 2: Same as Conjecture 1 when the polygon P is convex.

Eulerchain bounties:

• 100 Eulercoins for proving Conjecture 1. This implies Conjecture 2 is also true.
• 50 Eulercoins for disproving only Conjecture 1.
• 50 Eulercoins for proving only Conjecture 2.
• 100 Eulercoins for disproving Conjecture 2. This implies Conjecture 1 is also false.
• The bounties are valid till Dec 31 2021. If they are not resolved by Dec 31 2021, I will revisit this and update the bounties.

If you have any questions (or) solutions (or) counter-examples, leave a comment.

Happy Solving.

Conjecture 1: Given any convex polygon (v1, v2, …. v_n) drawn on a plane with integer edge lengths, there is a point x inside the polygon such that the euclidean distances between the pairs (x, v1), (x, v2), … (x, v_n) are all rational numbers.

Theorem: Conjecture 1 is true for n = 3.

Simple Homework: Prove Conjecture 1 for an equilateral triangle.

Conjecture 1 seems like a very natural geometry problem. Is it well-known ? If you know any references, please leave a comment or email me.

Citizen journalists, photo journalists and anyone anywhere in the world can use freebits to prove the authenticity of their photos, videos (captured using our iOS app) without ever revealing their real-world identity.

iOS app: https://apps.apple.com/us/app/freebits/id1582246045

Web app: http://freebits.app

A poll of 1,762 non-satellite TV stations and 3,379 radio outlets reveals journalists were threatened, assaulted, and even arrested at alarming rates across the U.S. in 2020. More details are in this article.

What is freebits ?

Freebits is a radically new kind of social media. It has built-in support for decentralized identities, privacy-preserving anonymous identities, AI-powered news aggregation, tamper-proof photos, videos, credentials and tamper-proof on-chain storage of socio-economic data (eg: unemployment numbers, prices of consumer goods, CPI to prevent data manipulation by governments and other centralized entities).Freebits is algorithm-free i.e., your posts will not be shadow-banned or hidden or suppressed.

Our mission is to enable journalists, creators, influencers, educators, podcasters, artists, politicians, activists, citizen journalists, photo journalists, data journalists, global leaders and everyone to speak freely to everyone globally, connect with their followers and get tips without any fear of censorship or shadow banning or de-platforming.

Freebits version 2.0 supports privacy-preserving anonymous accounts using public key cryptography. Username, email and password are not required. Citizen journalists, photo journalists and anyone anywhere in the world can use freebits to prove the authenticity of their photos, videos (captured using our iOS app) without ever revealing their real-world identity. Every photo and video shot using freebits app is a cryptographically-signed, verifiable and tamper-proof digital asset. The provenance and the digital rights of these assets are securely tracked using our Blockchain.

The intention of releasing this paper is to persuade everyone with factual & technical evidence that there is a global problem that must be addressed immediately & our solution is a superior method of solving it.

A pdf file of the white paper was released last month. It is available at http://shivakintali.org/freebits.pdf

Also, Happy Pride month to every global citizen… from the Freebits team.

Love, equality, human rights, free speech and freedom of expression for everyone.

Join Freebits and get free Euler cryptocurrency, proportional to the number of your twitter followers.

Only for the first 10,000 signups.

No hidden games. No scams. No spammy emails. You create your decentralized ID and own your private keys. You own your Euler. We will never ask you to send your bitcoin or any other crypto. We will never ask you to share your private keys or seed phrases.

For more details, please read my medium post https://kintali.medium.com/freebits-a-decentralized-global-public-square-89581235948