Quadratic congruence
= Quadratic congruence
{title2=$ax^2+bx+c\equiv0\pmod n$}
A quadratic congruence is a <modular congruence> defined by a degree-two <polynomial>, with solutions sought among <residue classes>. For odd $n$ and $a$ invertible modulo $n$, completing the square gives $(2ax+b)^2\equiv b^2-4ac\pmod n$. A <Jacobi symbol> of $-1$ for a <coprime> proposed square rules out solutions, whereas a <Jacobi symbol> of $1$ alone does not establish solubility for a composite modulus.