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x^n +y^n modulo n^2

Source: Kvant Magazine No. 9 2019 M2574

March 14, 2023
number theoryKvant

Problem Statement

Let n>1n>1 be a positive integer. Show that the number of residues modulo n2n^2 of the elements of the set {xn+yn:x,y∈N}\{ x^n + y^n : x,y \in \mathbb{N} \} is at most n(n+1)2\frac{n(n+1)}{2}.
[I]Proposed by N. Safaei (Iran)
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