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What Kind of Number is One?


Date: 12/06/2001 at 16:36:34
From: Mrs. Reed
Subject: One, primes and composites

What is one called since it is neither prime nor composite? I have 
tried numerous search engines and Web sites.


Date: 12/06/2001 at 20:45:56
From: Doctor Tom
Subject: Re: One, primes and composites

Hi,

Usually it is called a "unit."  In the integers, the number -1 is the 
only other unit. The primes are 2, 3, 5, ... and -2, -3, -5, ...  

Usually folks working with primes just use the positive integers, in 
which case 1 is the only unit. In more complex algebraic structures, 
there may be even more units. For example, in the Gaussian integers 
(which are complex numbers of the form: a + bi, where a and b are 
integers, the units are 1, -1, i, and -i. Note that 2 is no longer 
prime in the Gaussian integers:  2 = (1+i)(1-i).

- Doctor Tom, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Number Theory

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