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Pythagorean Triples

What are Pythagorean triple?

What are primitive Pythagorean triples?

What is the Pythagorean triples theorem?

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A Pythagorean triple is a set of 3 whole numbers (a, b, c) that satisfy the equation a2 + b2 = c2.

You might recognize that equation from the Pythagorean Theorem which says that the sum of the squares of the sides of a right triangle equals the square of the hypotenuse. Here, we're only interested in whole numbers that fulfill the equation. So, (3, 4, 5) is a Pythagorean triple because 32 + 42 = 9 + 16 = 25 = 52, but (1, 2, 3) is not because 12 + 22 = 1 + 4 = 5 ≠ 32.

There is an infinite number of Pythagorean triples. This can be shown by noting that if you take an known Pythagorean triple (a, ...

Solution Summary

The solution contains definitions and examples of Pythagorean triples, primitive Pythagorean triples, and the Pythagorean triples theorem.