Example
For example, examining the equation ax ≡ 2 (mod 6) with different values of a yields
Here d = gcd(3,6) = 3 but since 3 does not divide 2, there is no solution.
Here d = gcd(5,6) = 1, which divides any b, and so there is just one solution in {0,1,2,3,4,5}: x = 4.
Here d = gcd(4,6) = 2, which does divide 2, and so there are exactly two solutions in {0,1,2,3,4,5}: x = 2 and x = 5.
Read more about this topic: Linear Congruence Theorem
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)