Quadratic Congruence

A Congruence of the form

$$ax^2+bx+c\equiv 0\ \left({{\rm mod\ } {m}}\right),$$

where $a$, $b$, and $c$ are Integers. A general quadratic congruence can be reduced to the congruence

$$x^2\equiv q\ \left({{\rm mod\ } {p}}\right)$$

and can be solved using Excludents, although solution of the general polynomial congruence

$$a_mx^m+\ldots+a_2x^2+a_1x+a_0\equiv 0\ \left({{\rm mod\ } {n}}\right)$$

is intractable.

See also Congruence, Excludent, Linear Congruence