MathDB

Divisibility with quadratic form

Source: Kvant Magazine No. 9 2021 M2666

March 9, 2023

number theoryKvant

Problem Statement

Let

x{}

and

y{}

be natural numbers greater than 1. It turns out that

x^2+y^2-1

is divisible by

x+y-1

. Prove that

x+y-1

is composite.
From the folklore