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(a^2 - b^2 + k)/n is an integer.

Source: 2015 Saudi Arabia IMO TST I p3

July 24, 2020
number theoryInteger

Problem Statement

Let nn and kk be two positive integers. Prove that if nn is relatively prime with 3030, then there exist two integers aa and bb, each relatively prime with nn, such that a2−b2+kn\frac{a^2 - b^2 + k}{n} is an integer.
Malik Talbi
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