Imaginary prime number divisor

1. Jun 23, 2013

thedragonbook

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".

Last edited: Jun 23, 2013
2. Jun 23, 2013

Office_Shredder

Staff Emeritus
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

3. Jun 23, 2013

thedragonbook

I don't mean the imaginary number "i". I meant to say some thing that is just an idea - an imagination.

4. Jun 23, 2013

micromass

Staff Emeritus
Well, then it's not math. Locked.