Quadratic Residue

What

• $(p-a{)}^2\equiv a^2(\mathrm{mod}p)$
• $x^2=a(\mathrm{mod}p)$ has either no solutions or exactly 2 incongruent solutions modulo p; when p and a coprime

Properties

• $QR\times QR=QR$
• $QNR\times QR=QNR$
• $QNR\times QNR=QR$

Links

二次剩余 - 维基百科，自由的百科全书