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 Sep 15, 2018
edited by yasbib555  Sep 15, 2018
edited by yasbib555  Sep 15, 2018
edited by yasbib555  Oct 13, 2018
 #1
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1)  333^(5n - 2) mod 11 = 5 always, since:

(5n -2) =333, when n = 67, it follows that:

333^333 mod 11 =5

 Sep 15, 2018
 #2
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2)-

 

All numbers from 27 to 35 in base 10 are:
{1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022}in base 3
{43, 44, 45, 50, 51, 52, 53, 54, 55}in base 6
And the average is 31 in base 10

 Sep 15, 2018

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