Pythagorean Triplet

Instructions

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

a² + b² = c²

and such that,

a < b < c

For example,

3² + 4² = 5².

Given an input integer N, find all Pythagorean triplets for which a + b + c = N.

For example, with N = 1000, there is exactly one Pythagorean triplet for which a + b + c = 1000: {200, 375, 425}.

Implementation Notes

Range should return a list of all Pythagorean triplets with sides in the range min to max inclusive.

Sum should return a list of all Pythagorean triplets where the sum a+b+c (the perimeter) is equal to p. The three elements of each returned triplet must be in order, t[0] <= t[1] <= t[2], and the list of triplets must be in lexicographic order.

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Source

Problem 9 at Project Euler