Question: (4) Define Z, := {x E Zn : god(x, n) = 1}. Prove that Z,, is a group un- der multiplication mod n. You can

(4) Define Z, := {x E Zn : god(x, n) = 1}. Prove that Z,, is a group un- der multiplication mod n. You can assume that multiplication mod n is associative. Hint: Bezout's identity says that god(a, b) = 1 if and only if there exist integers x, y such that ax + by = 1. Consider this equation mod n

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