SOLUTION: . An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 dig

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Question 165475: . An “Armstrong number” is an n-digit number that is 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 13+ 53+33 =153 . What is the digit k in the Armstrong number 16k4?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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An “Armstrong number” is an n-digit number that is 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 13+ 53+33 =153 . What is the digit k in the Armstrong number 16k4?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
:
The example makes no sense as written, they mean 1^3 + 5^3 + 3^3 = 153
:
1^4 + 6^4 + k^4 + 4^4 = 1000 + 600 + 10k + 4
:
1 + 1296 + k^4 + 256 = 10k + 1604
:
1553 + k^4 = 10k + 1604
:
k^4 + 10k + 1553 - 1604 = 0
:
k^4 - 10k = 51
:
Since you only have 5 choices, just substitute until you have equality
k=3
3^4 - 10(3) =
81 - 30 = 51
:
The number 1634
:
CHeck 1^4 + 6^4 + 3^4 + 4^4 = 1634