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 2020-09-30, 13:44 #1 enzocreti   Mar 2018 17·31 Posts 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?
2020-09-30, 14:17   #2
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

3×11×43 Posts

Quote:
 Originally Posted by enzocreti 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.

 2020-10-10, 15:38 #3 R2357   "Ruben" Oct 2020 Nederland 2×19 Posts 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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