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06-17-2008, 11:20 PM
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| | Cyclotomic Extension We had the following problem for homework: let  prove that  lies in a cyclotomic extension.
(Without using Kronecker-Weber Theorem!)
I found a solution to this problem using quadradic Gauss sums, however this is not a course in number theory - it is a course on Galois theory, therefore my solution might be not acceptable. I will post it anyway because I want to print it out and give it to the class so which is why I am hanging it on the forum. I am interested in seeing other solutions.
__________________ And he (Elisha) went up from thence unto Bethel: and as he was going up by the way, there came forth little children out of the city, and mocked him, and said unto him, "Go up, thou bald head"; "go up, thou bald head". And he turned back, and looked on them, and cursed them in the name of the Lord. And there came forth two she-bears out of the wood, and tore up forty and two children of them.
Second Kings 2: 23-24
Last edited by ThePerfectHacker; 06-18-2008 at 08:38 AM.
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06-18-2008, 12:15 AM
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| | Hi
Here is your PDF file. Let me know if anything has to be modified. | | The following users thank flyingsquirrel for this useful post: | |  | 
06-18-2008, 08:39 AM
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| | Thank you very much!
There are two mistakes that I did. The first mistake appears in the proof of Theorem 1. The part in the parenthesis "If this fact is not familar ... "
After Theorem 3, "As a result ... ", that paragraph. It should say  and not  .
I edited my post above if it makes it any easier.
__________________ And he (Elisha) went up from thence unto Bethel: and as he was going up by the way, there came forth little children out of the city, and mocked him, and said unto him, "Go up, thou bald head"; "go up, thou bald head". And he turned back, and looked on them, and cursed them in the name of the Lord. And there came forth two she-bears out of the wood, and tore up forty and two children of them.
Second Kings 2: 23-24 | 
06-18-2008, 08:43 AM
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| | without your respect sir, can i ask why you can't do pdf?
i'm just curious.. Ü hope, you won't mind..
__________________ Venimus, vidimus, comemus tui crustuli
(We came, we saw, we ate your cookies)
"if it is for the one I love, I'd still fight the law." -Ichigo | 
06-18-2008, 08:47 AM
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| | Quote:
Originally Posted by kalagota without your respect sir, can i ask why you can't do pdf? | I can do a PDF, but why should I do it if I can find someone else to do it? 
Just joking! I never made a PDF before, I do not have a program which allows me to make a PDF, and I do not have LaTeX installed on my computer.
__________________ And he (Elisha) went up from thence unto Bethel: and as he was going up by the way, there came forth little children out of the city, and mocked him, and said unto him, "Go up, thou bald head"; "go up, thou bald head". And he turned back, and looked on them, and cursed them in the name of the Lord. And there came forth two she-bears out of the wood, and tore up forty and two children of them.
Second Kings 2: 23-24 | 
06-18-2008, 08:54 AM
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| | hahaha.. ok.
if you are interested in installing one, try downloading it here.. * > > > OVERJOYED < < < - LaTex.. LaTex.. LaTex
__________________ Venimus, vidimus, comemus tui crustuli
(We came, we saw, we ate your cookies)
"if it is for the one I love, I'd still fight the law." -Ichigo | 
06-18-2008, 09:11 AM
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| | Quote:
Originally Posted by ThePerfectHacker Thank you very much!
There are two mistakes that I did. The first mistake appears in the proof of Theorem 1. The part in the parenthesis "If this fact is not familar ... "
After Theorem 3, "As a result ... ", that paragraph. It should say  and not  .
I edited my post above if it makes it any easier. | I've corrected these two mistakes, see attachment. | | The following users thank flyingsquirrel for this useful post: | |  | 
06-18-2008, 09:38 AM
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| | You may want to increase the size of the document or modify layout options.
__________________  - Got trouble with LaTeX? Take a look.
- Make your partial integration (aka integration by parts) faster. Click here.
- How to prove limits by the
definition. | 
06-18-2008, 11:18 AM
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| | Thank you very much, you made it look like a professional written paper.
I am sorry that France lost yesterday.
__________________ And he (Elisha) went up from thence unto Bethel: and as he was going up by the way, there came forth little children out of the city, and mocked him, and said unto him, "Go up, thou bald head"; "go up, thou bald head". And he turned back, and looked on them, and cursed them in the name of the Lord. And there came forth two she-bears out of the wood, and tore up forty and two children of them.
Second Kings 2: 23-24 | 
06-18-2008, 12:31 PM
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Originally Posted by ThePerfectHacker Thank you very much, you made it look like a professional written paper. | Well that's why it's interesting to use LaTeX : once one knows the commands used to write equations (like \frac{}{} ...) it's really easy to make a document like this one. Quote: |
I am sorry that France lost yesterday.
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