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Project Euler Problem #009: Special Pythagorean triplet

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Project Euler Problem #009: Special Pythagorean triplet

(Problem Link)

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

a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup> For example, 3<sup>2</sup> + 4<sup>2</sup> = 9 + 16 = 25 = 5<sup>2</sup>.

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

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