The other day someone gave me a puzzle. It was a geometry type puzzle but I was a able to reduce it to a set of pythagorean triads. Essentually the problem turned out to be equilvalent to the following.(adsbygoogle = window.adsbygoogle || []).push({});

Find natural numbers a, b and c (each less than 42) such that {a, b, c} forms a Pythagorean traid and {(c-a), b} are also the first two elements of a second Pythagorean triad.

That is,a^2 + b^2 = c^2and(c-a)^2 + b^2 = n^2for some natural number n.

Since it was given that the problem had a solution it was a pretty easy matter of testing a few PT's to find the one that worked and I quickly found{a, b, c} = {7, 24, 25}.

Later it caught my attention that, {(c+a),b . }, also formed a Pythagorean triad, though this was not a requirement of the original problem. At first I suspected that this might be an implication of the other conditions but I was unable to deduce any such implication. So I thought I'd post it here and see if anybody else knew of any reason for that last PT other than just coincidence.

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# Is this result by coincidence or by implication?

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