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Math Help - congruence relation / residue classes

  1. #1
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    Question 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.
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  2. #2
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    Quote Originally Posted by PowerRanger69 View Post
    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
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