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。