Pythagorean triple

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

<math>x^2 + y^2 = z^2</math>

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

<math>3^2 + 4^2 = 9 + 16 = 25 = 5^2</math>
So, <math>3^2 + 4^2 = 5^2</math>

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.

no:Pythagoras’ læresetning#Pytagoreiske tripler