There are three six-digit numbers such that each is a 4th power of its sum of digits .

1. List them.
2. Each one has a certain peculiarity (or more than one). Try to define it.
3. Ignoring the 6-digits constraint , how many integers like that exist?

fourth root of 999999 = 31.62
fourth root of 111111 = 18.25

Therefore the sum of the digits must be between 19 and 31.  By calculating the fourth powers of the numbers between 19 and 31 and summing the digits yields the answers to be:

234256 summing to 22
390625 summing to 25
614656 summing to 28

Edited on August 15, 2012, 3:41 am

Posted by Chris, PhD on 2012-08-15 03:40:16