The question I am trying to solve is show that 5 is not irreducible in $Z[i]$. In order to solve this I need to show what makes up five, and then show neither of the two elements is a unit.
2026-05-14 09:56:01.1778752561
What does 5 equal in $Z[i]$
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$$5=5+0i$$ $$=(2+i)(2-i)$$ Now show that none of $2+i$ and $2-i$ is a unit.