Show that $a, b \in R^*, N(a) = N(ab)$ if, and only if, $a$ and $b$ are associate.
I tried to solve this using the fact that if $N(a) = N(ab)$ then $a \in <ab>.$ But I failed. Any Help?
2026-03-27 00:36:09.1774571769
Let $R$ be a euclidean domain, with norm function $N: R^{*} \to N$.
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