Any triple of positive integers a, b, and c, such that a squared + b squared= c squared.

three numbers whose sum of the squares of the two smaller numbers equals the square of the third number

An ordered set of three positive integers (a,b,c) such that a^2+b^2=c^2.

A set of three positive integers which satisfies the Pythagorean theorem. One example is {3, 4, 5}, since . Other examples are {6, 8, 10}, {5, 12, 13}, {8, 15, 17}, and {20, 21, 29}.

a set of three integers a, b, c which form the sides of a right angled triangle

a set of three positive whole numbers a, b, and c that are the lengths of the sides of a right triangle

a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c

Three positive integers that yield an equality in the pythagorean formula. If the three integers have no common integer factors, then the triple is a primitive. If the three integers have a common factor, then the triple is a multiple (Lesson 10.2).

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.