Let x in Z*_m (_m = subscript m) such that ord(x) = n. If x^i = x^j = (mod m), prove that i = j (mod n)????

An ESL Learner

2009-08-08 4:13 pm

Let x in Z*_m (_m = subscript m) such that ord(x) = n. If x^i = x^j = (mod m), prove that i = j (mod n)???????

Thx.

更新1:

Thanks, kb.

回答 (1)

kb

2009-08-08 4:32 pm

✔ 最佳答案

Since x^i = x^j mod m,
x^(i - j) = 1 mod m.

Hence, ord(x) | (i- j)
==> n | (i - j)
==> i = j mod n.

I hope that helps!

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