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Old 2020-09-30, 13:44   #1
enzocreti
 
Mar 2018

32·59 Posts
Default How to proof that numbers 18, 108, 1008,...will never be divisible by 6^4?

How to proof that numbers of the form 18, 108, 1008, 10008, 100008, 1000...0008 will never be divisible by 6^4?
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Old 2020-09-30, 14:17   #2
R. Gerbicz
 
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"Robert Gerbicz"
Oct 2005
Hungary

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Quote:
Originally Posted by enzocreti View Post
How to proof that numbers of the form 18, 108, 1008, 10008, 100008, 1000...0008 will never be divisible by 6^4?
For n>3 the
a(n)=10^n+8==8 mod 16 hence it won't be divisible by even 16=2^4 so not by 6^4.
And you can check the n<=3 cases easily since 6^4=1296>1008.
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Old 2020-10-10, 15:38   #3
R2357
 
"Ruben"
Oct 2020
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Smile 6^4

Or another way is that numbers ending in 1, 5 and 6 multiplied by a number ending by their end digit ends in that digit!
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