Problem 56293. Heronian Triangles with Consecutive Integral Sides and Integral Area

David Hill

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Hero's area formula for any triangle with sides a, b, c is: .
Heronian triangles are triangles having integral sides and integral area. Find Heronian triangles with consecutive sides. For example, H(1) would have sides 3,4,5 with area 6. Output the sum of the digits of the nth Heronian triangle's area. S(1)=6.

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