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Pythagorean Triples

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What are Pythagorean triple?

What are primitive Pythagorean triples?

What is the Pythagorean triples theorem?

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

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