## Digit fifth powers

### Problem 30

Published on Friday, 8th November 2002, 06:00 pm; Solved by 49082

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

> 1634 = 14 + 64 + 34 + 44
> 8208 = 84 + 24 + 04 + 84
> 9474 = 94 + 44 + 74 + 44

As 1 = 14 is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.