# 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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