# Pythagorean triple

In mathematics, a Pythagorean triple is a set of three positive integers which satisfy the equation (make the equation work):

${\displaystyle x^{2}+y^{2}=z^{2}}$

This equation is known as the Diophantine equation, and is related to Pythagoras' theorem. The lowest Pythagorean triple is [3, 4, 5] because:

${\displaystyle 3^{2}+4^{2}=9+16=25=5^{2}}$
So, ${\displaystyle 3^{2}+4^{2}=5^{2}}$

The next highest triple is [5, 12, 13] then [7, 24, 25], and so on. There is an infinite number of Pythagorean triples.

A Pythagorean triple always consists of:

• all even numbers, or

• two odd numbers and an even number.

A Pythagorean triple can never be made up of all odd numbers or two even numbers and one odd number.