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Math Help - existence of integers

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    existence of integers

    Suppose a,b are two integers with \gcd(m,n)=1. Prove that there exists integers m,n such that a^{m}+b^{n} \equiv 1  \mod{ab}
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    Quote Originally Posted by Chandru1 View Post
    Suppose a,b are two integers with \gcd(m,n)=1. Prove that there exists integers m,n such that a^{m}+b^{n} \equiv 1  \mod{ab}
    a^{\varphi(b)} + b^{\varphi(a)} is conguent to 1 mod a and also mod b, and hence mod ab ( \varphi is the Euler phi function).

    Edit. See this thread for further comments and links to previous occurrences of this question.
    Last edited by Opalg; February 6th 2010 at 04:13 AM. Reason: Found other references to this problem.
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