| To clarify: A Pythagorean Triangle (a,b,c) is a right triangle
with integer sides. The lengths of the sides are a, b, and c.
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| Since all primitive Pythagorean triples are of the form (2mn,m^2-n^2,m^2+n^2),
with m > n > 0, the problem is to find a non-trivial integral solution to
4 4 4 4
mn(m - n ) = xy(x - y )
I evaluated the left-hand side of this expression (modulo 2^32) for all m,n
with 256 >= m > n > 0, found the duplicates, and checked their values (this
time modulo 2^64). No solutions were found.
Perhaps someone would like to search further, or try proving that no such
solution exists.
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