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BD-BDMO 2021 Problem 11

    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

    Dataset text AI-MO AoPS. Quoted with source.

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