## Pythagorean Triplet Product

#### Problem

A Pythagorean triplet, $(a, b, c)$, is defined as a set of positive integers for which $a^2 + b^2 = c^2$.

Prove that for every triplet $abc$ is a multiple of sixty.

Problem ID: 301 (02 Jan 2007)     Difficulty: 3 Star

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