How many quadruples of positive integers $(a,b,m,n)$ are there such that all of the following statements hold? 1. $a,b<5000$ 2. $m,n<22$ 3. $gcd(m,n)=1$ 4. $(a^2+b^2)^m=(ab)^n$
Source: Bangladesh Mathematical Olympiad 2021 Problem 11
Tags: number theory
How many quadruples of positive integers $(a,b,m,n)$ are there such that all of the following statements hold? 1. $a,b<5000$ 2. $m,n<22$ 3. $gcd(m,n)=1$ 4. $(a^2+b^2)^m=(ab)^n$