'''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.'''

def sum_digit_power(exponent):
    answer = 0
    max_string = ''
    while len(max_string) < exponent:
        max_string += '9'
    while len(max_string) *(9**exponent) > int(max_string):
        max_string +='9'
    for num in range(2,int(max_string)):
        target =0
        target += num
        digit_power_sum = 0
        while digit_power_sum <= num:
            while num >9:
                digit = num % 10
                num = num //10
                digit_power_sum += digit ** exponent
            digit = num
            digit_power_sum += digit ** exponent
            if digit_power_sum == target:
                answer += target
            break
    return answer
print(sum_digit_power(5))