Pythagorean Triples And Generalizations

Math 304: Number Theory - Spring 2026

Introduction

A Pythagorean triple is a set of three positive integers (x, y, z) such that x² + y² = z². In this page, we'll explore how to find and analyze these triples using SageMath.

Finding Pythagorean Triples

Let's find all Pythagorean triples where x, y, z are positive and at most n:

Let's verify a few of these triples: