Find the 4th smallest heronian triangle(triangle with integer sides) with sides \(n\),\(n\) and \(n+1\) for a positive integer n. The perimeter of the triangle is "p" and the area is "a" for positive integers p and n.
\(a+p\) is a positive integer x.
Find \(x \mod(11*13*17)\).
Details and Assumptions
The first such triangle has area 12 and perimeter 16.
Hint: The answer is the sum of 2 perfect squares.