Congruence Equation

An equation of the form

(1)

where the values of  for which the equation holds are sought. Such an equation may have none, one, or many solutions. There is a general method for solving both the general linear congruence equation

(2)

and the general quadratic congruence equation

(3)

However, solution of the general polynomial congruence

(4)

is intractable. Note that any polynomial congruence will give congruent results when congruent values are substituted.