= Least quadratic nonresidue
{title2=$n(p)$}
For an <odd prime> $p$, the least quadratic nonresidue $n(p)$ is the smallest <positive integer> whose nonzero <residue class> is a <quadratic nonresidue> modulo $p$. For example, the nonzero <quadratic residues> modulo seven are $1,2,4$, so $n(7)=3$.
The least quadratic nonresidue is itself a <prime number>. Otherwise it has a <factorization> $n(p)=ab$ with $1<a,b<n(p)$. By minimality, both <residue classes> are <quadratic residues>, so $a\equiv u^2$ and $b\equiv v^2\pmod p$ would give $n(p)\equiv(uv)^2\pmod p$, a contradiction. This illustrates why multiplicative information can constrain a least exceptional <integer>.
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