This document provides a formula to calculate Pythagorean triples using integers a and w, where a is an integer or fractional number with a denominator that is a multiple of w, and w is an integer greater than or equal to 1. The formula calculates the sums of the squares of three terms (2aw + w), (2a^2w + 2aw), and (2a^2w + 2aw + w) to generate a Pythagorean triple for any integer value of w.

1. Formula to calculate Pythagorean triples
(2𝑎𝑤 + 𝑤)2
+ (2𝑎2
𝑤 + 2𝑎𝑤)2
= (2𝑎2
𝑤 + 2𝑎𝑤 + 𝑤)2
∀ 𝑤 ∈ ℤ ≥ 1
𝑎 is an integer or a fractional number whose denominator is a multiple of 𝑤.
By: José Acevedo Jiménez