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-   -   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!

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