# 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 $abc$.

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