How do we know that there are infinitly many Pythagorean triples?

Question

How do we know that there are infinitly many Pythagorean triples?

In: 2

Answer 1

Euclid’s proof:

Consider the identity n²+2n+1 = (n+1)²

Whenever 2n+1 is a square, this forms a Pythagorean triple. But 2n+1 comprises all the odd numbers

Every other square number is odd

There are an infinite number of odd squares

Hence there are an infinite number of Pythagorean triples.