Determine the number of distinct right-angled triangles such that its three sides are of integral lengths, and its area is $999$ times of its perimeter. (Congruent triangles are considered identical.)
Source: CGMO 2015 Q5
Tags: combinatorics, number theory
Determine the number of distinct right-angled triangles such that its three sides are of integral lengths, and its area is $999$ times of its perimeter. (Congruent triangles are considered identical.)