# Thread: congruence relation / residue classes

1. ## congruence relation / residue classes

I have an assignment I need some help to solve.

q, w, e ∈Z with q w (mod e)
Show that for every x ∈ Z, x>=1 the following holds:
q^x = (w^x)(mod e)

Thanks in adv.

2. Originally Posted by PowerRanger69
I have an assignment I need some help to solve.

q, w, e ∈Z with q w (mod e)
Show that for every x ∈ Z, x>=1 the following holds:
q^x = (w^x)(mod e)

Thanks in adv.

Well, q = w (mod e) means q = w + ne, for some integer n, or q - w = ne, so:

q^x - w^x = (q - w)(q^(x-1) + q^(x-2)*w +...+ w^(x-1)) = ne(T), where T is all the right long parentheses which, of course, is an integer.

Tonio