Date modified: Fri 2023-07-07 . 04:16 PM
Date created: Sat 2023-10-07 . 09:02 PM
# Admissible angles of a triangle satisfying Fermat's relations. It is well known that given a triangle with sides $0 < a\le b \le c$, then $a^{2}+b^{2}=c^{2}$ if and only if the angle opposing side $c$ is a right angle. (Pythagorean and its converse.) What about triangles satisfying $a^{n}+b^{n}=c^{n}$ for some other positive integer $n > 2$? What is the range of admissible angle opposing side $c$?