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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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
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