Consider the following functional equation: $$ f \left( x ^ 2 \right) = f ( x ) ^ 2 \text , $$ where $ f : \mathbb Z \to \mathbb Z $.
The only two solutions I could find so far are $ f ( x ) = 1 $ and $ f ( x ) = 0 $.
Are there any other solutions?
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4Please don't solve the question [...] it's an active competition problem and the poster of that question is trying to cheat on the USA national math olympiad. (edt) – Evan Chen Apr 13 '21 at 21:30