Abstract Algebra modular Arithmatic Proof

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Homework Help Overview

The discussion revolves around a proof in abstract algebra concerning modular arithmetic, specifically proving that \(10n \equiv 18 \mod 10\) for all \(n\) in the natural numbers.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of congruence in modular arithmetic and question how to apply this definition to the given problem. There is an inquiry into what needs to be shown regarding divisibility in the context of the proof.

Discussion Status

The discussion is ongoing, with participants seeking clarification on definitions and exploring the necessary conditions for the proof. Guidance has been offered regarding the application of the congruence definition, but no consensus or resolution has been reached yet.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can utilize or the methods they can employ in their reasoning.

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Homework Statement



Prove 10n ≡18 10 for all n ϵ N

Homework Equations




I have no idea where to even begin this proof.

The Attempt at a Solution


 
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What is the definition of [tex]a\equiv_n b[/tex] ?
 
it is said to be congruent integer modulo if n|a-b
 
So apply this definition to your problem. What are you trying to show? I.e., you are trying to show ____ is divisible by ____?

What would have to be true for a number to be divisible by ____?
 

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