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Find the remainder when you divide 3^100 by 23.

 

TYSM

 Mar 15, 2021
 #1
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-1

By Fermat's Little Theorem, the remainder is 9.

 Mar 15, 2021
 #2
avatar+130 
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This was incorrect, appreciate the effort

HelpPls123abc  Mar 17, 2021
 #3
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Let's  see if we  can find a pattern

 

Note  that  :

 

3^1 mod 23  = 3            3^12 mod 23   = 3       3^23 mod 23  =   3         3^34 mod 23 = 3

 

....

 

So...it  appears  that      3^(1 + 11n)  mod 23  =  3

 

Then

 

3^(1 + 11 * 9) mod 23  =  

 

3^(1 + 99) mod 23  = 

 

3^100 mod 23   =   3 

 

 

cool cool cool

 Mar 17, 2021
edited by CPhill  Mar 17, 2021

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