The domain of a function $f$ is the set of natural numbers. The function is defined as follows: $f(n) = n + \lfloor{\sqrt{n}}\rfloor$. Prove that for every natural number $m$ the following sequence contains at least one perfect square $m, f(m), f^{2}(m), f^{3}(m),...$
2026-04-03 16:29:27.1775233767
Show that sequence of composition of function $f(n) = n + \lfloor{\sqrt{n}}\rfloor$ contains at least one perfect square.
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