Difficult-looking Polynomial solved step by step | India IMO Training Camp 2019 Day 4 - Problem 1 скачать в хорошем качестве

Difficult-looking Polynomial solved step by step | India IMO Training Camp 2019 Day 4 - Problem 1

When you're going through this problem you'll see it naturally transform into another problem. Here we explained the thought process in detail and managed to fully transform it into another cool problem! Competition: India IMO Training Camp 2019 Day 4 - Problem 1 Here we attempted this problem step by step trying to get to Problem Statement: Determine all non-constant monic polynomials $f(x)$ with integer coefficients for which there exists a natural number $M$ such that for all $n \geq M$, $f(n)$ divides $f(2^n) - 2^{f(n)}$ TIMESTAMPS: 00:00 Intro 25/30 - 60/120 - 270 Take 5/10 00:27 Understanding the problem 01:27 Main fact for polynomials on the integers 02:10 Looking at prime factors of f(n) 02:25 Exploring ideas 04:05 Exploring one idea more deeply 07:50 Generalizing the main idea and realizing what we did 10:55 Two more ideas 18:01 Using the condition fully and solving the final problem 19:28 The problem we have to solve 20:00 Using the statement with a-b | f(a) - f(b) 20:35 Looking at the graph to help find f(0) 23:10 Getting more values and finishing 25:00 Reflecting on the problem 26:41 Thanks for problem solving :)