In Gauss'Lemma is it necessary for $a$ in $\left(\frac{a}{p}\right)$ to be a prime? I've checked a couple of books but there seems to be no restriction of this kind on $a$ just that $a$ and $p$ should be relatively prime. Any help would be appreciated thanks.
2026-03-28 02:42:48.1774665768
Problem regarding Gauss's Lemma
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No, it is not necessary.
The reason you are likely seeing this, is because since Legendre symbols are fully multiplicative it suffices to show that it is only true for when $a$ is a prime. Since all integers $a$ can be factored into primes and then decomposed into a product of Legendre symbols with primes on top.