From the Project Euler

*Problem 30:*

*Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:
1634 = 1 ^{4} + 6^{4} + 3^{4} + 4^{4}
8208 = 8^{4} + 2^{4} + 0^{4} + 8^{4}
9474 = 9^{4} + 4^{4} + 7^{4} + 4^{4}
As 1 = 1^{4} 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.*

**checked**

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