Is there a function $f: \mathbb N\to \mathbb N$ that satisfies $$f(f(n-1))=f(n+1)-f(n)$$ for $n \geq 2$? So far I just know that $f(n)>f(n-1)$ for $n \geq 2$.
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Sep 07 '19 at 09:13
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See https://math.stackexchange.com/questions/2183558/prove-that-there-is-no-function-f-mathbbz-ge-0-rightarrow-mathbbz-ge for case when $0 \in \mathbb{N}$ – Sil Sep 07 '19 at 11:25