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What is the remainder when 1009^109 is divided by 101? Thanks for help.

 Aug 11, 2016

Best Answer 

 #2
avatar+26396 
+5

What is the remainder when 1009^109 is divided by 101? Thanks for help.

 

1009109(mod101)|1009(mod101)=1(1)109(mod101)|(1)109=11(mod101)100(mod101)

 

laugh

 Aug 11, 2016
edited by heureka  Aug 11, 2016
edited by heureka  Aug 11, 2016
 #1
avatar+33654 
+5

mod(1009^1,101) = 100

mod(1009^2,101) = 1

mod(1009^3,101) = 100

mod(1009^4,101) = 1

mod(1009^5,101) = 100

...

mod(1009^109,101) = 100

.

 Aug 11, 2016
 #2
avatar+26396 
+5
Best Answer

What is the remainder when 1009^109 is divided by 101? Thanks for help.

 

1009109(mod101)|1009(mod101)=1(1)109(mod101)|(1)109=11(mod101)100(mod101)

 

laugh

heureka Aug 11, 2016
edited by heureka  Aug 11, 2016
edited by heureka  Aug 11, 2016

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