--description--

Let $f(N)$ be the number of points with integer coordinates that are on a circle passing through $(0,0)$, $(N,0)$,$(0,N)$, and $(N,N)$.

It can be shown that $f(10000) = 36$.

What is the sum of all positive integers $N ≤ {10}^{11}$ such that $f(N) = 420$?

--hints--

latticePointsOnACircle() should return 271204031455541300.

assert.strictEqual(latticePointsOnACircle(), 271204031455541300);

--seed--

--seed-contents--

function latticePointsOnACircle() {

  return true;
}

latticePointsOnACircle();

--solutions--

// solution required