Marinada '23

[lang = hr] Odredite sve $h: \mathbb{N} \rightarrow \mathbb{N}$ takve da $\forall x,y \in \mathbb{N}$ vrijedi \\ $$h{(x^2+y^2)}= h{(x)}h{(y)}$$ $$h{(x^2)} = (h{(x)})^2.$$ \\ Rješenje zapišite tako da napišete prvih $10$ članova niza $a_n$ \textbf{razdvojene zarezom} gdje je: $$a_n = \sum_{h \in H} h{(n)}$$ \\ $H$ je skup funkcija $h$ koje zadovoljavaju uvjete zadatka. [/lang] [lang = en] Determine all functions $h: \mathbb{N} \rightarrow \mathbb{N}$ such that $\forall x,y \in \mathbb{N}$ \\ $$h{(x^2+y^2)}= h{(x)}h{(y)}$$ $$h{(x^2)} = (h{(x)})^2.$$ \\ Give your solution by writing the first $10$ terms $a_n$ \textbf{separated by a comma} where: $$a_n = \sum_{h \in H} h{(n)}$$ \\ $H$ is the set of functions $h$ which satisfy the problem statement. [/lang]