- #1
nonequilibrium
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Homework Statement
Given that gcd(n,m)=1, prove that [itex]\mathbb Z_{nm}^\times = \mathbb Z_n^\times \oplus \mathbb Z_m^\times[/itex].
Homework Equations
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The Attempt at a Solution
I can prove both groups have the same amount of elements (using Euler's totient function), but I can't figure out how to prove the isomorphism. One way would be to construct the isomorphism, but I can't seem to find one.