Beginner: Modular Arithmetics basics

[ash009]

How to solve If A % 13 = 2 and B % 13 = 12, what is the value of (A * B) % 13?

 

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[AbdelRahmanShady]

A % 13 = 2 so A = 13k + 2 and B = 13 f + 12 expand and see remainder when dividing by 13

 

[pka]

A % 13 = 2 so A = 13k + 2 and B = 13 f + 12 expand and see remainder when dividing by 13

HERE Expand [imath](13k+2)(13f+12)[/imath] divide by [imath]13[/imath]. What is the remainder?

 

[Cubist]

HERE Expand [imath](13k+2)(13f+12)[/imath] divide by [imath]13[/imath]. What is the remainder?

I think @ash009 ought to show some work (or give some thoughts) concerning the question before we encourage @AbdelRahmanShady to provide an answer (via a longer than necessary route).

@ash009 try reading these identities for the modulo operation