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Math Help - Consider a right triangle with integer sides...

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    Consider a right triangle with integer sides...

    Consider a right triangle with integer sides having no common factor. Show that the average of the odd leg and the hypotenuse is a square number.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by NikoBellic View Post
    Consider a right triangle with integer sides having no common factor. Show that the average of the odd leg and the hypotenuse is a square number.
    The odd leg of a right triangle is of the form  m^2-n^2 and in your case  (m,n)=1 . The hypotenuse of the same triangle is then  m^2+n^2 .

    Now what is  \frac{(m^2+n^2)+(m^2-n^2)}{2} ?
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