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Math Help - Pythagorean Triples Proof

  1. #1
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    Pythagorean Triples Proof

    Prove that the longer leg of a Pythagorean triple can never be twice the shorter leg.
    I know that I need to prove this indirectly. I am just having trouble coming to a contradiction.
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  2. #2
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    If one leg is twice the other leg, the hypotenuse is (5^.5) times the shorter leg.
    That would not be a whole number.
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  3. #3
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    Quote Originally Posted by bearej50 View Post
    Prove that the longer leg of a Pythagorean triple can never be twice the shorter leg.
    I know that I need to prove this indirectly. I am just having trouble coming to a contradiction.
    If x^2+y^2 = (2x)^2 \implies y^2 = 3x^2 and this is the contradition because that equation is impossible for positive integers.
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