Congruence Rules
In the following we are only talking about integers: Positive, Negative, and zero.

Last Up date: 2005 October 17
Started: Mon 04-08-09 11:19:37

Still from Gauss.

Addition Rule
If a ≡ b (mod m) and c ≡ d (mod m)
then a + c ≡ b + d (mod m)
observe (a + c) - (b + d) = (a - b) + (c - d)

Subtraction Rule follows from the above.

By repeated application of the addition rule it follows:
One can add an arbitrary set of congruences for the same modulus.

Another application of the addition rule is simply adding a given congruence to itself k times. Thus we have:

If a ≡ b (mod m)
then ka ≡ kb (mod m)

A congruence may be multiplied by an arbitrary integer

Write several numeric examples, and observe the above "rules".
When, you are sure you are competent: go to the next page.

Contact me at:
My phone #'s
For comments call, or e-mail me. Go to My Home Page or TOP of this page.