Project Euler #009 - Special Pytagorean triplet

Problem

A Pythagorean triplet is a set of three natural numbers, \(a < b < c\), for which,
\(\qquad a^2 + b^2 = c^2\)
For example, \(3^2 + 4^2 = 25 = 5^2\)
There exists exactly one Pythagorean triplet for which \(a + b + c = 1000\).
Find the product \(abc\).

PE#009 ...

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