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n|(a+b)^2,(b+c)^2,(c+a)^2

Source: Assara 2024 S7

October 14, 2024
number theory

Problem Statement

Find all positive integers nn for such the following condition holds: "If aa, bb and cc are positive integers such are all numbers a2+2ab+b2, b2+2bc+c2, c2+2ca+a2 a^2+2ab+b^2,\ b^2+2bc+c^2, \ c^2+2ca+a^2 are divisible by nn, then (a+b+c)2(a+b+c)^2 is also divisible by nn." G.M.Sharafetdinova
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