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

Because we construct infinitely many. Pick any two distinct natural numbers n and m. Then we have a pythagorean triple by

a=m^(2)-n^(2)

b=2mn

c=m^(2)+n^(2)