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Old 2013-11-05, 06:25   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Default prime producing polynomial x^2 + x + 41

Hello Internet Mathematical Community,

I want to mention a little webpage that I recently got off my chest.

https://sites.google.com/site/mattc1...ing-polynomial

Surely these few lines do not do it justice.

(RDS please hold your silence)

Regards,
Matt A.
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Old 2013-11-05, 13:11   #2
R.D. Silverman
 
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Quote:
Originally Posted by MattcAnderson View Post
Hello Internet Mathematical Community,

I want to mention a little webpage that I recently got off my chest.

https://sites.google.com/site/mattc1...ing-polynomial

Surely these few lines do not do it justice.

(RDS please hold your silence)

Regards,
Matt A.
The website is currently content free. What is its purpose?
The polynomial you cite has been well studied. What do you hope to add or
contribute?

If you are really interested in the mathematics that is associated with this
polynomial, then you need to study why the fact that Q(sqrt(-163)) has class number 1 is fundamental to the study of this polynomial. Indeed.
Do you even know where the number -163 comes from in this context??
Do you know what a class number is?

Before you try to discuss this polynomial you need to learn some of the
math behind it. If you can't be bothered to do that then please stop the
discussion.

I would start by reading the Hardy & Wright chapter on quadratic fields.
You then need to study binary quadratic forms, composition of forms,
class numbers and genera. Harvey Cohn wrote an excellent book:
"Advanced Number Theory" [Dover!] discussing all of these things. I can
recommend other books on algebraic number theory as well if you like.
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Old 2013-11-05, 15:49   #3
Batalov
 
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"Serge"
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Quote:
Originally Posted by MattcAnderson View Post
Surely these few lines do not do it justice.

(RDS please hold your silence)
Moved to misc.math.

Matt, just because you don't understand a word of what RDS is saying doesn't give you right to shut him up.

Indeed, these few lines don't do the subject any justice. Why don't you first read mathworld, wikipedia, OEIS, etc? What are you planning to add to what is already known, and how?
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Old 2013-11-06, 01:48   #4
MattcAnderson
 
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"Matthew Anderson"
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Hi,

I have noticed some properties of the polynomial expression x^2 + x + 41, which I will call h(x).

For example, this expression is never divisible by a positive integer less than 40.

Here is why. Using an even and odd argument, we can show that h(x) is never divisible by 2.

If the input, x, is even, then h is odd.
Similarly, if the input, x, is odd, then h is again odd.
And odd numbers are not divisble by two.

Also, an argument with divisibility by three can be made.
No matter if x is 0,1,or 2 mod 3 the output is never 0 mod 3.

And so on with the primes up to 40.

If h(x) is not divisible by any primes below 40, then it is not divisible by any counding number less than 40.

Please let me know if you understand so far.

Regards,
Matt

Also, the power point document linked above is again linked here -

https://docs.google.com/viewer?a=v&p...I4ODU1NWQ5ZDk1

For what its worth,
M.C.A.
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Old 2013-11-06, 03:43   #5
CRGreathouse
 
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Quote:
Originally Posted by MattcAnderson View Post
For example, this expression is never divisible by a positive integer less than 40.

Here is why. [...]

Please let me know if you understand so far.
This is easy to see. If it were in a math paper this wouldn't even get a proof, just a line "By modular considerations, we can see ...".

Last fiddled with by CRGreathouse on 2013-11-06 at 03:45
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Old 2013-11-06, 13:26   #6
R.D. Silverman
 
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Quote:
Originally Posted by MattcAnderson View Post
Hi,

I have noticed some properties of the polynomial expression x^2 + x + 41, which I will call h(x).

For example, this expression is never divisible by a positive integer less than 40.


Here is why. Using an even and odd argument, we can show that h(x) is never divisible by 2.

<snip>
It is more basic than what you suggest.

The coefficients are positive and f(x) := x^2 + x + 41 is trivially greater than
43 for x > 1. Further for ANY polynomial g(x), if a | g(x) then a | g(x + k*a)
for all k \in Z.
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Old 2013-11-06, 18:14   #7
MattcAnderson
 
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Thank you for the constructive feedback.

And also, I have read the three references suggested in the thread.

So much for this dead project.

Regards,
Matt
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Old 2013-11-07, 12:18   #8
R.D. Silverman
 
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Quote:
Originally Posted by MattcAnderson View Post
Thank you for the constructive feedback.

And also, I have read the three references suggested in the thread.
Impossible. I suggested reading part of Hardy & Wright as well as
H. Cohn's entire book.

And yes. I know the likelihood that you will take my advice.
People in this thread seem to view the actual LEARNING of mathematics
as a chore to be avoided.
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Old 2013-11-07, 18:30   #9
science_man_88
 
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Quote:
Originally Posted by R.D. Silverman View Post
People in this thread seem to view the actual LEARNING of mathematics
as a chore to be avoided.
miscellaneous math is a subforum, but if you teach my pharmaceutical calculations teacher ( or professor) how to do 60/40 in their head so they can teach me I'll be fine with that. I tend to shortcut to get the answer quicker for some of what we are doing.

Last fiddled with by science_man_88 on 2013-11-07 at 18:34
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Old 2013-11-08, 09:05   #10
NBtarheel_33
 
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Quote:
Originally Posted by science_man_88 View Post
miscellaneous math is a subforum, but if you teach my pharmaceutical calculations teacher ( or professor) how to do 60/40 in their head so they can teach me I'll be fine with that. I tend to shortcut to get the answer quicker for some of what we are doing.
Able me no parse to text this. In other words, say what?!
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Old 2013-11-08, 11:39   #11
science_man_88
 
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Quote:
Originally Posted by NBtarheel_33 View Post
Able me no parse to text this. In other words, say what?!
  • miscellaneous math is a subforum
  • my pharmaceutical calculations ( aka pharmacy math) teacher can't do simple math in their head. ( yes I'm in a pharmacy technology course to become a technician)
  • I tend to shortcut the math compared to how they want it done.
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