Pythagorean Triples Calculator

Generate Pythagorean triples (a, b, c) with a^2 + b^2 = c^2 using Euclid's formula a = m^2 - n^2, b = 2mn, c = m^2 + n^2, or check whether three integers form a triple.

Frequently Asked Questions

What is a Pythagorean triple?

Three positive integers a, b, c with a squared plus b squared equals c squared. The triple is primitive if a, b, c have no common factor greater than 1.

How do I find primitive triples?

Use Euclid's formula with m greater than n, both positive integers, with greatest common divisor one and opposite parity. Every primitive Pythagorean triple arises this way exactly once.

Why does Euclid's formula work?

Because (m squared minus n squared) squared plus (2 m n) squared equals (m squared plus n squared) squared is a polynomial identity, derived from the factorization of c squared minus a squared.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.