Understanding Congruency and Its Applications

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Discussion Overview

The discussion revolves around the concept of congruency in number theory, specifically focusing on the relationship between numbers in modular arithmetic. Participants explore the implications of one number being congruent to another under a given modulus.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant seeks a simpler explanation of congruency, particularly in the context of whether 333 being congruent to 3 mod 10 allows for replacing 333 with 3.
  • Another participant clarifies that congruency means both numbers yield the same remainder when divided by the modulus, in this case, 10.
  • A later reply expresses relief that the concept is simpler than initially thought, indicating a desire for further understanding.
  • One participant references another thread for additional context or examples related to the topic.

Areas of Agreement / Disagreement

Participants appear to agree on the basic definition of congruency, but there is an underlying uncertainty about the broader implications and applications of this concept.

Contextual Notes

The discussion does not delve into the formal mathematical properties or theorems related to congruency, which may limit the understanding of its applications.

Who May Find This Useful

Readers interested in number theory, modular arithmetic, or those seeking clarification on congruency concepts may find this discussion beneficial.

johnnyICON
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I'm having a bit of trouble understanding what it means for one number to be congruent to another. I have this more technical definition but I was wondering if anyone could put it into more simple terms.

What I really want to know is that if say 333 is congruent to 3 mod 10, does that mean that 333 is equivalent to 3 mod 10? Can I replace 333 by just 3?

I am looking a lot of examples in my notes and I see numbers being replaced by their congruencies, is that allowed?
 
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Nope,it means that both 333 and 3 give the same remainder when divided by 10,naely 3.

Daniel.
 
That's all? : Nothing more? Well that makes things more simple then. I was thinking there was more to it. Thanks.
 

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