problem30

Problem 30: Digit fifth powers

Problem Statement

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.

Comments

The first thing here is to establish upper/lower bounds: a lower bound could be 10, and as for an upper bound 6*9⁵ is a six-digit number (354294), so any answer must be less than that.

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Yeah, nothing too unusual here. Did find the convenient .pow function on most number-like types.