Difference between revisions of "Linear congruence"

Revision as of 10:36, 15 August 2006

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.

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.

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-== Linear Congruences ==
 A '''Linear Congruence''' is a congruence mod p of the form
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 , where a, b, c, and p are constants, and x is the variable.
+==Example 1: How to solve==
+Say <math>5x\equiv 7\pmod{8}</math>.  Find <math>x</math>.
+Solution:
+<math>5x\equiv 7\equiv 15\pmod{8}</math>, so
+<math>x\equiv 3\pmod{8}</math>, because 5 is relatively prime to 8, we can divide by it.