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Math Help - Congruence

  1. #1
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    Congruence

    For all integers a and positive integers m and n, if a is congruent to 1 (mod m) and a is congruent to 1 (mod n), then a is congruent to 1 (mod mn)
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  2. #2
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    Quote Originally Posted by leilani13 View Post
    For all integers a and positive integers m and n, if a is congruent to 1 (mod m) and a is congruent to 1 (mod n), then a is congruent to 1 (mod mn)

    False:  a = 7\,,\,n=6\,,\,m=3

    Tonio
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  3. #3
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    Quote Originally Posted by leilani13 View Post
    For all integers a and positive integers m and n, if a is congruent to 1 (mod m) and a is congruent to 1 (mod n), then a is congruent to 1 (mod mn)
    Of course tonio is right; and fyi if we change mn to lcm(m,n) then it becomes true.
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by leilani13 View Post
    For all integers a and positive integers m and n, if a is congruent to 1 (mod m) and a is congruent to 1 (mod n), then a is congruent to 1 (mod mn)
    This is true iff  (m,n)=1 .

    See here.
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