# Pythagorean Triplets

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 such that $$a + b + c = 1000$$. Find the value of $$c$$.

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