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M2666

Part of Kvant 2021

Problems(1)

Divisibility with quadratic form

Source: Kvant Magazine No. 9 2021 M2666

3/9/2023
Let xx{} and yy{} be natural numbers greater than 1. It turns out that x2+y2−1x^2+y^2-1 is divisible by x+y−1x+y-1. Prove that x+y−1x+y-1 is composite.
From the folklore
number theoryKvant