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Math Help - Special right triangle...

  1. #1
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    Special right triangle...

    Another one I had fun with...I'll make SURE I post it properly!

    Pythagorean right triangle ABC, sides a, b and c (a < b < c).
    a = u^2 + u
    b = v^2 + v
    c = w^2 + w

    Find smallest case.
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  2. #2
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    Re: Special right triangle...

    Hey Wilmer.

    The constraints (u^2 + u) + (v^2 + v) = w^2 + w with u < v < w (since all positive and a < b < c) is used to minimize the value of u and make it a pythagorean triple which means that u^2 + u + v^2 + v = x^2 for some integer x.

    The question now is whether you want to try and apply some number theory or whether you want to program a computer to find solutions (since you are only looking for the first case and not a general case).
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  3. #3
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    Re: Special right triangle...

    Agree.
    The first one I found: a = 17556 (u=132), b = 20592 (v=143) and c = 27060 (w=164).

    Quite large, and was really looking for confirmation that there isn't a smaller one.
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