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Math Help - prove

  1. #1
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    Question prove

    prove that if n and m are relatively prime, gcd(n,m)=1, then |U(n)|*|U(m)|=|U(nm)|
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  2. #2
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    Quote Originally Posted by mandy123 View Post
    prove that if n and m are relatively prime, gcd(n,m)=1, then |U(n)|*|U(m)|=|U(nm)|
    Define \phi: \mathbb{Z}_{nm}^{\times}\to \mathbb{Z}_n^{\times} \times \mathbb{Z}_m^{\times} by \phi( [x]_{nm}) = ( [x]_n, [x]_m).
    Show this is well-defined.
    Now prove this is a bijection by using Chinese remainder theorem.
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