Question

Two consecutive positive integers form part of a Pythagorean triple. Always, never, or sometimes?

Answer 1

I believe the answer is sometimes. The most well known Pythagorean triple is 3,4,5.

3^2+4^2=5^2

9+16=25

25=25

However this is not always the case, for example,

8,15,17

is also a Pythagorean triple, but has no positive, consecutive, integers.