Home Competitions ISL 2020 A6
Determine all functions f : Z → Z f: \mathbb{Z} \rightarrow \mathbb{Z} f : Z → Z f a 2 + b 2 ( a + b ) = a f ( a ) + b f ( b ) for every a , b ∈ Z f^{a^{2}+b^{2}}(a+b)=a f(a)+b f(b) \text { for every } a, b \in \mathbb{Z} f a 2 + b 2 ( a + b ) = a f ( a ) + b f ( b ) for every a , b ∈ Z f n f^{n} f n n th n^{\text {th }} n th f f f f 0 ( x ) = x f^{0}(x)=x f 0 ( x ) = x f n + 1 ( x ) = f ( f n ( x ) ) f^{n+1}(x)=f\left(f^{n}(x)\right) f n + 1 ( x ) = f ( f n ( x ) ) n ⩾ 0 n \geqslant 0 n ⩾ 0
Dataset text NuminaMath olympiads . Quoted with source.
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f(x) = x + 1 \text{ or } f(x) \equiv 0
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