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What is the remainder when 5^30*4^30 is divided by 7?

 Jun 22, 2022
 #1
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5^30 * 4^30   =

 

(5 * 4)^30  =

 

20^30

 

 

Note that

20^1  mod 7  =   6

20^2 mod 7  =   1

20^3 mod 7 =     6

20^4  mod 7  =  1

 

So......it appears that

 

20^(2n) mod 7  =  1

 

So

 

20^(2 * 15)  mod 7  =     20^30  mod 7   =  1

 

 

 

 

cool cool cool

 Jun 22, 2022

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