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Math Help - Pythagorean Triples

  1. #1
    Junior Member
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    Pythagorean Triples

    Question:
    Verify that3, 4, 5 is the only primitive Pythagorean triple involving consecutive positive integers.
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  2. #2
    Senior Member
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    Apr 2009
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    Atlanta, GA
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    Trouble with Triples

    Suppose a^2+b^2=c^2 are integers. Without loss of generality, 0<a<b<c.

    x^2+(x+1)^2=(x+2)^2
    2x^2+2x+1=x^2+4x+4
    x^2-2x-3=0
    (x-3)(x+1)=0
    x=3 or x=-1

    But we have already supposed all values are positive, so we discard (-1,0,1) and are left only with (3,4,5).
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