Pythagorean Numbers

Pythagorean numbers [pə‚thag·ə′rē·ən ′nəm·bərz]

(mathematics)

Positive integersx, y,andzwhich satisfy the equationx²+y²=z². Also known as Pythagorean triple.

---

Pythagorean Numbers 

triples of natural numbers such that if the lengths of the sides of a triangle are proportional or equal to the numbers of such a triple, the triangle is a right triangle. By the converse to the Pythagorean theorem, it is sufficient if the numbers satisfy the Diophantine equation x² + y² = z². An example of such a triple is x = 3, y = 4, and z = 5. All triples of relatively prime Pythagorean numbers can be obtained from the formulas

x = m² – n² y = 2mn z = m² + n²

where m and n are integers and m > n > 0.