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Math Help - Suppose that gcd(a,b)=1 and that a|n and b|n. Prove that ab|n.

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    Suppose that gcd(a,b)=1 and that a|n and b|n. Prove that ab|n.

    Suppose that gcd(a,b)=1 and that a|n and b|n. Prove that ab|n.
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    Quote Originally Posted by qtpipi View Post
    Suppose that gcd(a,b)=1 and that a|n and b|n. Prove that ab|n.
    If gcd(a,b)=1 then there are integers r,s such that ra + sb = 1. If a|n and b|n then there are integers k,l such that n = ka = lb. You can then deduce that
    rka + skb = k,
    b(rl + sk) = k,
    ab(rl + sk) = ka = n,
    so n is a multiple of ab.
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