ag-gipp/GoUldI

<math xmlns='http://www.w3.org/1998/Math/MathML' display='inline'><semantics><mrow><mrow><mo>(</mo><mfrac><mi>a</mi><mi>p</mi></mfrac><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><mrow><mtable displaystyle="false" columnalign="left left" rowspacing="0.5ex" rowlines="none"><mtr><mtd><mn>1</mn></mtd> <mtd><mtext> if </mtext><mi>a</mi><mtext> is a quadratic residue modulo </mtext><mi>p</mi><mtext> and </mtext><mi>a</mi><mi><mo>≡</mo≯</mi><mn>0</mn><mrow><mo lspace="mediummathspace">(</mo><mo rspace="thinmathspace">mod</mo><mi>p</mi><mo rspace="mediummathspace">)</mo></mrow><mo>,</mo></mtd></mtr> <mtr><mtd><mo lspace="verythinmathspace" rspace="0em">−</mo><mn>1</mn></mtd> <mtd><mtext> if </mtext><mi>a</mi><mtext> is a quadratic non-residue modulo </mtext><mi>p</mi><mo>,</mo></mtd></mtr> <mtr><mtd><mn>0</mn></mtd> <mtd><mtext> if </mtext><mi>a</mi><mo>≡</mo><mn>0</mn><mrow><mo lspace="mediummathspace">(</mo><mo rspace="thinmathspace">mod</mo><mi>p</mi><mo rspace="mediummathspace">)</mo></mrow><mo>.</mo></mtd></mtr></mtable></mrow></mrow></mrow><annotation encoding='application/x-tex'>\left(\frac{a}{p}\right) =  \begin{cases}  1 & \text{ if } a \text{ is a quadratic residue modulo } p \text{ and } a \not\equiv 0\pmod{p}, \\ -1 & \text{ if } a \text{ is a quadratic non-residue modulo } p, \\  0 & \text{ if } a \equiv 0 \pmod{p}.   \end{cases}</annotation></semantics></math>