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An “Armstrong number”


sserendipty

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  • 11 months later...
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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