1. ## An Armstrong number

An Armstrong number is an n-digit number that i s equal to the sum of the nth powers of
its individual digits. For example, 153 is an Armstrong number because it has 3 digits and
1^3 + 5^3+ 3^3= 153 . What is the digit k in the Armstrong number 1, 6k4?  Reply With Quote

2. ## Re: An Armstrong number Originally Posted by sserendipty An “Armstrong number” is an n-digit number that i s equal to the sum of the nth powers of
its individual digits. For example, 153 is an Armstrong number because it has 3 digits and
1^3 + 5^3+ 3^3= 153 . What is the digit k in the Armstrong number 1,6k4?
1,6k4 is a 4-digit number.
So, 1^4 + 6^4 + k^4 + 4^4 = 16k4
Evaluate: 1 + 1296 + k^4 + 256 = 16k4
Simplify: 1553 + k^4 = 16k4

Whatever k is, it must be the case that the UNITS digit of k^4 is 1, so that 1553 + k^4 = 16k4
Test some values..
k = 1: 1^4 = 1, so we get: 1553 + 1 = 1614 NO GOOD
k = 3: 3^4 = 81, so we get: 1553 + 81 = 1634 WORKS!!

Cheers,
Brent  Reply With Quote

3. ## Re: An Armstrong number

You know, I need to take a GRE courses for the university, hope it wouldn't be so hard for me.  Reply With Quote