Saturday, 28 September 2013

nice triple

Call a triple (a, b, c) of positive integers a nice triple if a, b, c forms a non-decreasing arithmetic progression, gcd(b, a) = gcd(b, c) = 1 and the product abc is a perfect square. Prove that given a nice triple, there exists some other nice triple having at least one element common with the given triple.
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