Problem 30

Digit Fifth Powers

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.

各位数字的五次幂

令人惊讶的是，只有三个数可以写成其各位数字的四次幂之和：
$1634 = 1^{4} + 6^{4} + 3^{4} + 4^{4}$
$8208 = 8^{4} + 2^{4} + 0^{4} + 8^{4}$
$9474 = 9^{4} + 4^{4} + 7^{4} + 4^{4}$

由于 $1 = 1^{4}$ 并不是求和，所以这里不计入内。

上面这三个数的和是 $1634 + 8208 + 9474 = 19316$ 。

找出所有可以写成其各位数字的五次幂之和的数，并求这些数的和。