Difficult-looking Polynomial solved step by step | India IMO Training Camp 2019 Day 4 - Problem 1
Автор: Shefs of Problem Solving
Загружено: 2025-09-23
Просмотров: 547
Описание:
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 :)
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