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