# Problem 218: Perfect right-angled triangles

![graphic](img218.gif)

Consider the right angled triangle with sides a=7, b=24 and c=25. The
area of this triangle is 84, which is divisible by the perfect numbers 6
and 28. Moreover it is a primitive right angled triangle as gcd(a,b)=1
and gcd(b,c)=1. Also c is a perfect square. We will call a right angled
triangle perfect if -it is a primitive right angled triangle -its
hypotenuse is a perfect square We will call a right angled triangle
super-perfect if -it is a perfect right angled triangle and -its area is
a multiple of the perfect numbers 6 and 28. How many perfect
right-angled triangles with c≤1016 exist that are not super-perfect?