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Is the number $|m^2+1-n^2|$ is a perfect square?

Source: Moldova TST 2001

August 6, 2023
number theory

Problem Statement

Let mm and nn{} be positive integers of the same parity such that n2−1n^2-1 divides ∣m2+1−n2∣|m^2+1-n^2|. Is the number ∣m2+1−n2∣|m^2+1-n^2| is a perfect square?
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