Understand the problem Z be the set of all integers. Determine all f : Z -> Z such that, for all integers a, b Source of the problem IMO 2019 Problem 1 Topic Functional Equation Difficulty Level 5 out of 10 Suggested Book Functional Equation and How to Solve...

Magic Squares are infamous; so famous that even the number of letters on its Wikipedia Page is more than that of Mathematics itself. People hardly talk about Magic Rectangles. Ya, Magic Rectangles! Have you heard of it? No, right? Not me either! So, I set off to...

Do you know that CLOCKS add numbers in a different way than we do? Do you know that ROTATIONS can also behave as numbers and they have their own arithmetic? Well, this post is about how clocks add numbers and rotations behave like numbers. Consider the clock on earth....

This is proof from my book – my proof of my all-time favorite true result of nature – Pick’s Theorem. This is the simplest proof I have seen without using any high pieces of machinery like Euler number as used in The Proofs from the Book. Given a...

Inspired by the book of Precalculus written in a dialogue format by L.V.Tarasov, I also wanted to express myself in a similar fashion when I found that the process of teaching and sharing knowledge in an easy way is nothing but the output of a lucid discussion between...

This problem is known as Collatz Conjecture. Consider the following operation on an arbitrary positive integer: If the number is even, divide it by two.If the number is odd, triple it and add one. The conjecture is that no matter what value of the starting number, the...