Math problem

[ZultanofZex]

Can anyone help out with this one?

I have a question and I am not really sure how to answer could you take a look? I need some serious help with this question becuase I am having trouble finding the definitions and and resaons behind the definitions.

Q) Are all Gaussian whole numbers whose norm is a normal prime number also a gaussian prime number?

(from a swedish question so sorry about the translation)

A Gaussian Prime NUmber(definition)

If a gaussian prime number is a gaussian whole number which has an absolute value greater than 1 och which isn't the product of Gaussian whole numbers with a absolute value less than the product of the Gaussian whole numbers.

Does anyone have a clue how I should approach this question??

PLease please help me

 

[nihilistic]

Yes, its norm has to be a prime (in N) congruent to 1 modulo 4 for it to be prime. There is a proof of the existence of an unique solution to a^2 + b^2 = p in natural numbers where p is a prime (in N) congruent to 1 modulo 4 and a >= b. I can post it if you want.

 

[nihilistic]

D'oh, I seem to have omitted the trivial exceptions: 1+i and others ...

Basically, a Gaussian Integer is prime iff one of the follwing conditions is true:

1. its norm is a prime in the form 4k+1 where k is in N

2. it is a prime in Z whose absolute value is in the form 4k-1 where k is in N

3. its norm is 2

 

[ZultanofZex]

Cheers! Gibberish to me, but I will pass it along to my girlfriend, she is the one doing math.

Thanx alot for the quick reply

 

[ZultanofZex]

what is N? - this is the girlfriend question again

 

[nihilistic]

Originally posted by ZultanofZex
what is N? - this is the girlfriend question again

The set of Natural Numbers: 1, 2, 3, 4, ...

 

[ZultanofZex]

Thank you...I think my girlfriend like you better then me, now...

She is wondering if you are free for math lessons anytime soon....

.:worshp:

 

[nihilistic]

Originally posted by ZultanofZex
She is wondering if you are free for math lessons anytime soon....

Just post it here or use PM.

 

[Smaasnekje]

I AM NEVER GOING TO DO MATHS IN SCHOOL AFTER THE 20th OF JUNE!! HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA! :spam: that was a neccesary evil... Sorry..

 

[ZultanofZex]

Are all prime numbers also gaussian prime numbers?

 

[nihilistic]

Originally posted by ZultanofZex
Are all prime numbers also gaussian prime numbers?

No. Only the primes whose absolute values are in the form 4k+3.

2 = (1+i) (1-i)

Since any prime p in the form 4k+1 can be written as a^2 + b^2.

(a + bi) (a - bi) = p

Examples:
(2 + i) (2 - i) = 5
(3 + 2i) (3 - 2i) = 13
(4 + i) (4 - i) = 17

 

[ZultanofZex]

Once again, thank you.

My girlfriend also wonders if you, apart from being a wizard of math, is rich, handsome and tall. If you are, she want's your phone number......

and I will start hunting you down


cheers

 

[onejayhawk]

I'm Getting in a little late on this, but this site may help Ask Doctor Math.

J

 

[Perfection]

What is a Gaussian whole number?

 

[onejayhawk]

A number which is of the from a+bi, where a and b are whole numbers.

 

[nihilistic]

Originally posted by ZultanofZex
My girlfriend also wonders if you, apart from being a wizard of math, is rich, handsome and tall. If you are, she want's your phone number......

and I will start hunting you down

I'm 5' 10", definitely handsome, not particularly rich, but possesses immense agility (i.e.: evading getting beat up).

Originally posted by onejayhawk
I'm Getting in a little late on this, but this site may help Ask Doctor Math.

It depends on what you want. If you are not afraid of notations, there is also the more organized and higher level MathWorld. If you want faster replies or are doing something completely new in the field, sci.math at Google is also a good choice.

 

[Perfection]

Okay so then what is an Och and a norm

 

[nihilistic]

Originally posted by Perfection
Okay so then what is an Och and a norm

Here, norm(A) is defined as A multiplied by the conjugate of A. And the conjugate of a+bi is defined to be a - bi.