--description--

A positive integer, $n$, is divided by $d$ and the quotient and remainder are $q$ and $r$ respectively. In addition $d$, $q$, and $r$ are consecutive positive integer terms in a geometric sequence, but not necessarily in that order.

For example, 58 divided by 6 has a quotient of 9 and a remainder of 4. It can also be seen that 4, 6, 9 are consecutive terms in a geometric sequence (common ratio $\frac{3}{2}$).

We will call such numbers, $n$, progressive.

Some progressive numbers, such as 9 and 10404 = ${102}^2$, also happen to be perfect squares. The sum of all progressive perfect squares below one hundred thousand is 124657.

Find the sum of all progressive perfect squares below one trillion (${10}^{12}$).

--hints--

progressivePerfectSquares() should return 878454337159.

assert.strictEqual(progressivePerfectSquares(), 878454337159);

--seed--

--seed-contents--

function progressivePerfectSquares() {

  return true;
}

progressivePerfectSquares();

--solutions--

// solution required