Why does $p$ have to be prime on a finite field $\{0,1,...,p-1\}$?
I'm looking at content on elliptic curve cryptography, and the guy brings up finite fields from $0$ to $p-1$ where $p$ is prime.
Why is $p$ prime? What's the reasoning behind this?
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https://math.stackexchange.com/questions/72856 – 311411 Oct 29 '21 at 03:37
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If $n=a\cdot b$, where $a,b\not\in{1,n}$, then $a\cdot b\equiv 0\bmod n$; that shows $\mathbb Z/n\mathbb Z$ is not a field – J. W. Tanner Oct 29 '21 at 03:58