Legendre symbol

《初等数论》 · 第 204 页

$\left(\dfrac{d}{p}\right)$ 称为模 $p$ 的 Legendre 符号。

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《Introduction to Analytic Number Theory》 · 第 179 页 · Section 9.2「Legendre's symbol and its properties」，Definition

Let $p$ be an odd prime. If $n\not\equiv0\pmod p$ we define Legendre's symbol $\left(\frac np\right)$ as follows: it is $1$ if $n$ is a quadratic residue mod $p$, and $-1$ if $n$ is a quadratic nonresidue mod $p$. If $n\equiv0\pmod p$ we define $\left(\frac np\right)=0$.