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NT FE with perfect squares

Source: MEMO 2022 T7

September 2, 2022
number theoryfunctional equation

Problem Statement

Determine all functions f:N→Nf : \mathbb {N} \rightarrow \mathbb {N} such that ff is increasing (not necessarily strictly) and the numbers f(n)+n+1f(n)+n+1 and f(f(n))−f(n)f(f(n))-f(n) are both perfect squares for every positive integer nn.
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