Does there exist a function $f : \mathbb{N} \rightarrow \mathbb{N}$ such that for every $n \ge 2$, \[f (f (n - 1)) = f (n + 1) - f (n)?\]
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Tags: function, algebra unsolved, algebra
Does there exist a function $f : \mathbb{N} \rightarrow \mathbb{N}$ such that for every $n \ge 2$, \[f (f (n - 1)) = f (n + 1) - f (n)?\]