>A prime is defined as a number divisible only by itself and 1
>According to this then, than can a prime be difined as a number
divisible
>only by itself and one "unit"?
>So why is -3i composite?
>It is only divisible by 3 and -i , or by a product of one (1) + prime
>int., and one (1) unit.
>
>J. Zylstra
>[EMAIL PROTECTED]
In ring theory, a unit is any element with a multiplicative inverse. In
the ring of Gaussian integers (a+bi with a,b in Z) the units are 1, -1,
i, -i. An associate of an element x is the product of x with some unit.
An irreducible element is defined as one having no divisors other than
the units and its associates. An element is prime if it has the property
that whenever it divides a product, it must also divide one of the
factors. This definiton of primality differs a little from the general
usage, but it is explained by the fact that primality and irreducibility
are equivalent in the ring of integers. This isn't true in some other
rings.
There is a set of rules for determining primes in the Gaussian integers
based on primes in the integers, but it has been awhile since I've
looked at them and I don't have the book handy.
What did this have to do with Mersenne primes, again? :)
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