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Thread: An “Armstrong number”

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    Trying to make mom and pop proud
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    An “Armstrong number”

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    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?

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    GRE-GMAT Instructor Brent Hanneson's Avatar
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    Re: An “Armstrong number”

    Quote Originally Posted by sserendipty View Post
    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!!

    Answer: k = 3

    Cheers,
    Brent

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    Trying to make mom and pop proud
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    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.

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