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

For example,

There exists exactly one Pythagorean triplet for which,

Find the product abc.

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A Pythagorean triplet is a set of three natural numbers, for which, a < b < c \qquad 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. Solution This I wasn't quite sure how ...