20200930, 13:44  #1 
Mar 2018
7^{2}×11 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?

20200930, 14:17  #2  
"Robert Gerbicz"
Oct 2005
Hungary
3^{2}×179 Posts 
Quote:
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. 

20201010, 15:38  #3 
"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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