--description--

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
• its area is a multiple of the perfect numbers 6 and 28.

How many perfect right-angled triangles with $c ≤ {10}^{16}$ exist that are not super-perfect?

--hints--

perfectRightAngledTriangles() should return 0.

assert.strictEqual(perfectRightAngledTriangles(), 0);

--seed--

--seed-contents--

function perfectRightAngledTriangles() {

  return true;
}

perfectRightAngledTriangles();

--solutions--

// solution required