Imaginary prime number divisor

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Discussion Overview

The discussion revolves around the implications of assuming the existence of an imaginary number that can divide a prime number, with a focus on the conceptual nature of this imaginary number as a purely imaginative construct rather than a mathematical entity like the imaginary unit "i".

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant proposes exploring the implications of an imaginary number that divides a prime number, emphasizing its imaginative nature.
  • Another participant questions whether the number must be imaginary or if any complex number could suffice, referencing the properties of Gaussian integers and their relation to prime numbers.
  • A later reply reiterates the original intent of the term "imaginary" as a conceptual idea rather than a mathematical construct.
  • One participant concludes that if the concept is purely imaginative, it does not pertain to mathematics, suggesting a potential closure of the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the "imaginary" number in question, with some focusing on mathematical implications while others emphasize its conceptual basis. The discussion remains unresolved regarding the validity and relevance of the initial premise.

Contextual Notes

The discussion highlights a lack of clarity regarding the definitions of "imaginary" and "complex" in this context, as well as the implications of treating an imaginative concept within mathematical frameworks.

thedragonbook
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What would be the implications of assuming the existence of an imaginary number that can divide a prime number and is related to the number it is dividing? By imaginary I mean a number that is just in our imagination and not the imaginary number "i".
 
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The question is a little weird. Does it have to be an imaginary number or can it be any complex number? For example 2 = (1+i)(1-i).The Gaussian integers which are all numbers of the form a+bi for a and by integers form a ring which can be used to deduce some interesting number theoretic facts, for example every prime equivalent to 1 mod 4 can be expressed as the sum of two squares

http://en.wikipedia.org/wiki/Gaussian_integer
 
I don't mean the imaginary number "i". I meant to say some thing that is just an idea - an imagination.
 
thedragonbook said:
I don't mean the imaginary number "i". I meant to say some thing that is just an idea - an imagination.

Well, then it's not math. Locked.
 

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