Linear congruence

A Linear Congruence is a congruence mod p of the form

$ax+b\equiv c\pmod{p}$

, where a, b, c, and p are constants, and x is the variable.

Example I: How to solve

Say $5x\equiv 7\pmod{8}$ . Find $x$ .

Solution:

$5x\equiv 7\equiv 15\pmod{8}$ , so

$x\equiv 3\pmod{8}$ , because 5 is relatively prime to 8, we can divide by it.