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I think so. Let $f$ be a homomorphism from $\mathbb Z[[x]] $ to $\mathbb Z$. WRONG: Let $f(x^i)=a_i$. Then since $f(1+x+x^2...) \in \mathbb Z$, we must have $a_i=0$ for $i\gg 0$. So each map can be identified with an element in $\mathbb Z[x]$.