Problem 218

Perfect right-angled triangles

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 c10^{16} exist that are not super-perfect?

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These problems are part of
Project Euler
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