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m+n-1|m^2+n^2-1 implies m+n-1 composite (Slovenia 1997 3rd Grade P1)

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May 3, 2021
number theoryDivisibility

Problem Statement

Suppose that m,nm,n are integers greater than 11 such that m+n−1m+n-1 divides m2+n2−1m^2+n^2-1. Prove that m+n−1m+n-1 cannot be a prime number.
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