---
id: 5900f5331000cf542c510046
challengeType: 5
title: '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.
## Instructions
## Tests
```yml
tests:
- text: euler455() should return 450186511399999.
testString: 'assert.strictEqual(euler455(), 450186511399999, "euler455() should return 450186511399999.");'
```
## Challenge Seed
```js
function euler455() {
// Good luck!
return true;
}
euler455();
```