---
id: 5900f5331000cf542c510046
title: 'Problem 455: Powers With Trailing Digits'
challengeType: 5
forumTopicId: 302129
dashedName: problem-455-powers-with-trailing-digits
---

# --description--

Let f(n) be the largest positive integer x less than 109 such that the last 9 digits of nx form the number x (including leading zeros), or zero if no such integer exists.

For example:

f(4) = 411728896 (4411728896 = ...490411728896) f(10) = 0 f(157) = 743757 (157743757 = ...567000743757) Σf(n), 2 ≤ n ≤ 103 = 442530011399 Find Σf(n), 2 ≤ n ≤ 106.

# --hints--

`euler455()` should return 450186511399999.

```js
assert.strictEqual(euler455(), 450186511399999);
```

# --seed--

## --seed-contents--

```js
function euler455() {

  return true;
}

euler455();
```

# --solutions--

```js
// solution required
```