--description--

Let $f(n)$ be the largest positive integer $x$ less than ${10}^9$ such that the last 9 digits of $n^x$ form the number $x$ (including leading zeros), or zero if no such integer exists.

For example:

$$\begin{align} & f(4) = 411\,728\,896 (4^{411\,728\,896} = ...490\underline{411728896}) \\ & f(10) = 0 \\ & f(157) = 743\,757 (157^{743\,757} = ...567\underline{000743757}) \\ & Σf(n), 2 ≤ n ≤ 103 = 442\,530\,011\,399 \end{align}$$

Find $\sum f(n)$, $2 ≤ n ≤ {10}^6$.

--hints--

powersWithTrailingDigits() should return 450186511399999.

assert.strictEqual(powersWithTrailingDigits(), 450186511399999);

--seed--

--seed-contents--

function powersWithTrailingDigits() {

  return true;
}

powersWithTrailingDigits();

--solutions--

// solution required