--description--

If we calculate $a^2\bmod 6$ for $0 ≤ a ≤ 5$ we get: 0, 1, 4, 3, 4, 1.

The largest value of a such that $a^2 ≡ a\bmod 6$ is $4$.

Let's call $M(n)$ the largest value of $a < n$ such that $a^2 ≡ a (\text{mod } n)$. So $M(6) = 4$.

Find $\sum M(n)$ for $1 ≤ n ≤ {10}^7$.

--hints--

idempotents() should return 39782849136421.

assert.strictEqual(idempotents(), 39782849136421);

--seed--

--seed-contents--

function idempotents() {

  return true;
}

idempotents();

--solutions--

// solution required