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Math Help - Abstract algebra proof

  1. #1
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    Abstract algebra proof

    If a and b are natural numbers, (a,b) = 1, and ab is square, show that a and b are squares.
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  2. #2
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    Quote Originally Posted by Zennie View Post
    If a and b are natural numbers, (a,b) = 1, and ab is square, show that a and b are squares.
    ab has a unique prime number decomposition. Since ab is even, every prime number is to an even power. Now look at the prime number decompositions of a and b. Since (a,b)= 1, they have NO prime numbers in common.
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