Question 1
Let $a,b,c$ be positive integers such that $a^2+b^2=c^2$, where $0\lt a\lt b\lt c$. The ordered triple $(a,b,c)$ is called a Pythagorean triple. For example, $(3,4,5)$ is a Pythagorean triple. How many Pythagorean triples $(a,b,c)$ are there such that $a+b+c=120$?