Prove that any odd number can be a leg in a Pythagorean trip

Prove that any odd number can be a leg in a Pythagorean triple. (b)Prove that any even number can be a leg in a Pythagorean triple.

Solution

we can proof both the proofs in a single way

it is a property of triples that

out of the 3 sides

one side is even and other two sides are odd. Or all sides are even. These relationships hold because square of an odd number isan odd number and square of an even is even,and since all two are even one has to be even , and sine two are odd one has to even