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Number of integers (a,b,m,n) for holding Conditions

Source: Bangladesh Mathematical Olympiad 2021 Problem 11

February 26, 2022
number theory

Problem Statement

How many quadruples of positive integers (a,b,m,n)(a,b,m,n) are there such that all of the following statements hold? 1. a,b<5000a,b<5000 2. m,n<22m,n<22 3. gcd(m,n)=1gcd(m,n)=1 4. (a2+b2)m=(ab)n(a^2+b^2)^m=(ab)^n
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