This was a fun little challenge!! I realize that I could have done this in fewer tools, but I wanted to make it flexible enough to handle different numbers of digits.
Extending to other digit counts:
I added a workflow constant to try the same pattern with other digit counts...
There are no solutions for 2 digits (where digit1^2 + digit2^2 = number)
Four digits: (e.g. 1^4 + 6^4 + 3^4 + 4^4 = 1,634)
Seven digits: (at this point, with 9,000,000 possible numbers, it had a 38.5 s run time)
Example: 1^7 + 7^7 + 4^7 + 1^7 + 7^7 + 2^7 + 5^7 = 1 + 823,543 + 16,384 + 1 + 823,543 + 128 + 78,125 = 1,741,725
Intermediate Challenge can mean a great deal of things as this one wasn't too bad for me.