The Pythagorean number theorem is the basis for modern number theory. Modern number theory is that branch of mathematics concerned with properties and relationships of numbers. This includes much of mathematics and more specifically mathematical analysis and is generally limited to the study of integers or other sets that possess properties of all integers. The Pythagoreans carried out extensive mathematical investigations concerned with numbers, mainly of odd and even numbers and of prime and square numbers, that established a scientific foundation for mathematics. Their results and beliefs are summarized into the Pythagorean number theorem.

Pythagoras was a Greek mathematician thought to have been born in about 500 B.C.. Although originally born on the island of Samos, Pythagoras was thought to have moved to Crotona in about 530 B.C. where he founded a movement known as Pythagoreanism. The disciples of this movement are believed to...