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Quadratic Congruence

A Congruence of the form

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

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

\begin{displaymath}
x^2\equiv q\ \left({{\rm mod\ } {p}}\right)
\end{displaymath}

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

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

is intractable.

See also Congruence, Excludent, Linear Congruence




© 1996-9 Eric W. Weisstein
1999-05-25