sserendipty Posted November 28, 2015 Share Posted November 28, 2015 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? Quote Link to comment Share on other sites More sharing options...
Brent Hanneson Posted November 19, 2016 Share Posted November 19, 2016 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 Quote Link to comment Share on other sites More sharing options...
Sarabey Posted December 13, 2016 Share Posted December 13, 2016 You know, I need to take a GRE courses for the university, hope it wouldn't be so hard for me. Quote Link to comment Share on other sites More sharing options...
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