--description--

Let r be the remainder when ${(a − 1)}^n + {(a + 1)}^n$ is divided by $a^2$.

For example, if $a = 7$ and $n = 3$, then $r = 42: 6^3 + 8^3 = 728 ≡ 42 \ \text{mod}\ 49$. And as n varies, so too will r, but for $a = 7$ it turns out that $r_{max} = 42$.

For $3 ≤ a ≤ 1000$, find $\sum{r}_{max}$.

--hints--

squareRemainders() should return 333082500.

assert.strictEqual(squareRemainders(), 333082500);

--seed--

--seed-contents--

function squareRemainders() {

  return true;
}

squareRemainders();

--solutions--

// solution required