Pythagorean Triplet2026-04-28

My Solution: Exercism Pythagorean Triplet solution

Instructions

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

a^2 + b^2 = c^2

and such that:

a < b < c

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}.

Return a list of lists, such as [[a, b, c]]. The order of the outer list does not matter.

Solution

def triplets_with_sum(number):

    # We can solve this by combining the two equations:
    # c = number - a - b
    # a^2 + b^2 = c^2
    # which gives:
    # b = (number^2 - 2 * number * a) / (2 * (number - a))

    triplets = []

    for a in range(1, number // 3):
        numerator = (number ** 2) - (2 * number * a)
        denominator = 2 * (number - a)

        if numerator % denominator == 0:
            b = numerator // denominator
            c = number - a - b

            if a < b < c:
                triplets.append([a, b, c])

    return triplets

Syntax Notes

• The sum condition lets us write c in terms of a, b, and number.
• Substituting that into a^2 + b^2 = c^2 gives a direct formula for b.
• range(1, number // 3) is enough because a must be the smallest value in the triplet.
• The numerator % denominator == 0 check ensures b is a whole number.
• The a < b < c check filters out duplicates and keeps the triplet in ascending order.