Solve Modular Arithmetic Homework: 12^9 mod71

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Homework Help Overview

The discussion revolves around solving the modular arithmetic problem of finding 12^9 mod 71. Participants are exploring the properties of modular exponentiation and the calculations involved.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to break down the problem using properties of exponents but expresses confusion about the steps involved. Some participants provide calculations for 12^2 mod 71 and its implications for 12^8 mod 71, while others question the validity of these calculations.

Discussion Status

The discussion is ongoing, with participants sharing their reasoning and calculations. There is a mix of attempts to clarify the steps and some uncertainty about the calculations being presented. No consensus has been reached yet.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the depth of explanation and exploration of concepts.

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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 don't understand what he did so can someone explain how to do it in a very basic way.?
Thank you v much.
 
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12^2 mod 71=2 mod 71. So 12^8 mod 71=2^4 mod 71.
 
how come 12^2mod71=2mod71 ??
 
Because 12^2=144. 144 mod 71=2 mod 71.
 

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