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Let n be a positive integer, and consider U(n), the group of units in Z sub n. We know that
theta(n) = |U(n)|.
a) Assume a is an element of U(n). Prove that if r is equivalent to s mod theta(n), then a^r is equivalent to a^s mod n.
b) Is the converse of a) true, in other words, is the following true: If a is an element of U(n) and a^r is equivalent to a^s mod n, then r is equivalent to s mod theta(n).
Last edited by dchilow (2007-11-12 12:11:42)
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