Hello everybody :)
This is my first question in this forum, so hopefully I'm doing it right. I wonder if there is an easy formula to calculate how many pythagorean triangles have the same circumfirence. Co for example:
A rectangular triangle with circumfirence 36 can only be one with sides 9 and 12 and hypothenusa 15. So there's only 1 possibility as can easily be found out by trial and error.
However, for a triangle with circumfirence 120 there are 3 possibilies:
Sides 30 and 40, hypothenusa 50. Sides 20 and 48, hypothenusa 52. Sides 24 and 45, hypothenusa 51.
(This also is not difficult to see.)
A Triangle with circumfirence 20 of course doesn't have pytagorean properties.
I'm looking for the general case. Is there a formula, or could I develop one, to find out the number of these pythagorean triads?