Wading Herons

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.


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