Pythagorean Triplets

A Pythagorean triplet is a set of three natural numbers, a<b<ca < b < c, for which a2+b2=c2{ a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }. For example, 32+42=9+16=25=52{ 3 }^{ 2 }+{ 4 }^{ 2 }=9+16=25={ 5 }^{ 2 }.

There exists exactly one Pythagorean triplet such that a+b+c=1000a + b + c = 1000. Find the value of cc.

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