# Elements of Primitive Pythagorean Triples Modulo 4/Corollary

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## Corollary to Elements of Primitive Pythagorean Triples Modulo 4

In every Pythagorean triple, at least one element is a multiple of $4$.

## Proof

From Solutions of Pythagorean Equation, any Pythagorean triple is such that all elements are a multiple of the elements in some primitive Pythagorean triple.

As the latter must have an even element which is a multiple of $4$, such an element when multiplied by some integer will still be a multiple of $4$.

$\blacksquare$