I would like to know how do homomorphisms from $\mathbb{Z}[X] $ to $\mathbb{Z}_5$ look like. I know that there should be $5$ of them since $1$ must be mapped to $1$ and $\mathbb{Z}_5$ has $5$ elements. However I don't know do they look like.
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1Related: https://math.stackexchange.com/questions/935877/how-to-prove-that-the-evaluation-map-is-a-ring-homomorphism – Brian Moehring Jan 10 '22 at 10:15
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Oh, the proof refers to the homomorphism that I'm lookig for! Am I right? @BrianMoehring – blackkay1 Jan 10 '22 at 10:34