mersenneforum.org

mersenneforum.org (https://www.mersenneforum.org/index.php)
-   enzocreti (https://www.mersenneforum.org/forumdisplay.php?f=156)
-   -   How to proof that numbers 18, 108, 1008,...will never be divisible by 6^4? (https://www.mersenneforum.org/showthread.php?t=26023)

enzocreti 2020-09-30 13:44

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?

R. Gerbicz 2020-09-30 14:17

[QUOTE=enzocreti;558357]How to proof that numbers of the form 18, 108, 1008, 10008, 100008, 1000...0008 will never be divisible by 6^4?[/QUOTE]

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.

R2357 2020-10-10 15:38

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!


All times are UTC. The time now is 10:35.

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.