# Problem 9: Special Pythagorean triplet

A Pythagorean triplet is a set of three natural numbers, *a* < *b* < *c*, for which,

*a*^{2} + *b* ^{2} = *c*^{2}

For example, 3^{2} + 4^{2} = 9 + 16 = 25 = 5^{2}.

There exists exactly one Pythagorean triplet for which *a* + *b* + *c* = 1000.

Find the product *abc*.

## JavaScript

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