Pythagorean triple

mathematics

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July 13, 2026

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A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². This relationship is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).12

A primitive Pythagorean triple is one where a, b, and c have no common factors other than 1. The most well-known example is the triple (3, 4, 5), as 3² + 4² = 9 + 16 = 25, which equals 5². Formulas exist to generate all primitive Pythagorean triples. These triples have several interesting properties, such as one of the legs always being divisible by 3 and 4, and the product of a, b, and c always being divisible by 60.32

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mathematics
Geometric and algebraic problems
(Such solutions are sometimes called Pythagorean triples.) A tablet in the Columbia University Collection presents a list of 15 such triples (decimal equivalents are shown in parentheses at the right; the gaps in the expressions for h, b, and d separate the place values in the sexagesimal numerals):
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(Such solutions are sometimes called Pythagorean triples.) A tablet in the Columbia University Collection presents a list of 15 such triples (decimal equivalents are shown in parentheses at the right; the gaps in the expressions for h, b, and d separate the place values in the sexagesimal numerals):
Read More

mathematics
The pre-Euclidean period
…sets of numbers (now called Pythagorean triples): if one takes two whole numbers p and q, both being even or both odd and such that pq is a square number, then a = (p − q)/2, b = Square root of√pq, and c = (p+ q)/2. As Euclid proves in Book X…
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…sets of numbers (now called Pythagorean triples): if one takes two whole numbers p and q, both being even or both odd and such that pq is a square number, then a = (p − q)/2, b = Square root of√pq, and c = (p+ q)/2. As Euclid proves in Book X…
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