Prove that the expression is a perfect square – math.stackexchange.com

Prove that the expression is a perfect square – math.stackexchange.com

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Let $m$ be a natural number. Define $f(m) = m + \lfloor\sqrt{m}\rfloor$. Prove that at least one of the number among $m, f(m), f^2(m), \ldots$ is a perfect square. Here $f^k(m)$ denotes the ...

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