Triangles with non rational sides and integral area

Problem 390

Published on 23 June 2012 at 08:00 pm [Server Time]

Consider the triangle with sides √5, √65 and √68. It can be shown that this triangle has area 9.

S(n) is the sum of the areas of all triangles with sides √(1+b2), √(1+c2) and √(b2+c2) (for positive integers b and c ) that have an integral area not exceeding n.

The example triangle has b=2 and c=8.


Find S(1010).

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