Project Euler Problem 30 Solution

Question

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

1634=14+64+34+448208=84+24+04+849474=94+44+74+44\begin{aligned} 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 \end{aligned}

As 1=141=1^4 is not a sum it is not included.

The sum of these numbers is 1634+8208+9474=193161634+8208+9474=19316.

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

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