In a right triangle, all the sides are positive integers. One of the legs is equal to 180. How many different possible values are there for the hypotenuse?
The better question is, "How many pythagorean triples are there which have one of the legs as 180, but not the hypotenuse?"
There are up to two of them, I believe.
One I know is {19,180,181}. That's one...
We can plug 180 into the pythagorean triple finder, and there are a couple rules here: https://primes.utm.edu/glossary/page.php?sort=PrmPythagTriples#:~:text=The%20square%20of%20the%20length,5%2C12%2C13).
Play around with that a little and tell us what you find!