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Modular arithmetic

  • Thread starter sara_87
  • Start date
  • #1
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Homework Statement



find: 12^9 mod71

Homework Equations





The Attempt at a Solution



=12(12^8) mod71
= 12mod71 x 12^8mod71
= 12 x (12^2)^4mod 71

Now i'm stuck. My teacher solved it but i dont understand what he did so can someone explain how to do it in a very basic way.?
Thank you v much.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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12^2 mod 71=2 mod 71. So 12^8 mod 71=2^4 mod 71.
 
  • #3
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how come 12^2mod71=2mod71 ??
 
  • #4
Dick
Science Advisor
Homework Helper
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618
Because 12^2=144. 144 mod 71=2 mod 71.
 

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