Possibility of a Separate Forum for NT & Abstract Algebra

In summary, the conversation discusses the need for separate forums for number theory and abstract algebra and the demonstration that there are infinitely many n for which both 6n + 1 and 6n - 1 are composite without using the Chinese Remainder Theorem. The participants suggest using n = 35x - 1 or n = 36k^3 as examples.
  • #1
The Chaz
206
0
1. There should be a separate (sub)forum for NT. ... and one for abstract algebra, for that matter!

2. Show that there are infinitely many n such that both 6n + 1 and 6n - 1 are composite. Without CRT, if possible.

My work... let n = 6^{2k}.
Then 6n \pm 1 = 6^{2k + 1} \pm 1...
Hmm. Having a hard timing finding the LaTexification button from my iPhone...
To be continued.
 
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  • #2
Let n = 35x - 1, for any positive integer x.

6n + 1 = 6(35x - 1) + 1 = 210x - 5 = 5(42x - 1)
6n - 1 = 6(35x - 1) - 1 = 210x - 7 = 7(30x - 1)

QED

PS: there is no LaTeX yet
 
  • #3
Bacterius said:
Let n = 35x - 1, for any positive integer x.

6n + 1 = 6(35x - 1) + 1 = 210x - 5 = 5(42x - 1)
6n - 1 = 6(35x - 1) - 1 = 210x - 7 = 7(30x - 1)

QED

PS: there is no LaTeX yet

Slick.
I also like n = 36k^3.
Then 6n \pm 1 is a sum/difference of cubes...
 

FAQ: Possibility of a Separate Forum for NT & Abstract Algebra

What is the purpose of having a separate forum for NT and Abstract Algebra?

The purpose of having a separate forum for NT (Number Theory) and Abstract Algebra is to create a dedicated space for discussions, questions, and resources specifically related to these two branches of mathematics. This can help foster a more focused and specialized community and provide a platform for individuals with a strong interest in these subjects to connect and collaborate.

Who would benefit from a separate forum for NT and Abstract Algebra?

A separate forum for NT and Abstract Algebra would benefit mathematicians, researchers, students, and anyone with a strong interest in these subjects. It can also be beneficial for individuals looking to learn more about these topics or seeking help with specific problems or concepts.

How would a separate forum for NT and Abstract Algebra be different from other math forums?

A separate forum for NT and Abstract Algebra would be different from other math forums in that it would have a narrower focus and cater specifically to discussions and questions related to these two branches of mathematics. This would allow for a more specialized and in-depth discussion of topics, as well as a more targeted audience with a deeper understanding of these subjects.

Would the forum be open to all levels of knowledge in NT and Abstract Algebra?

Yes, the forum would be open to all levels of knowledge in NT and Abstract Algebra. It would provide a platform for beginners to ask questions and learn from more experienced individuals, as well as a space for experts to share their knowledge and engage in more advanced discussions.

How can I contribute to the NT and Abstract Algebra forum?

There are several ways to contribute to the NT and Abstract Algebra forum. You can actively participate in discussions, share your knowledge and resources, and help answer questions from other members. You can also suggest new topics for discussion or provide feedback to improve the forum. Your contributions can help build a thriving community for NT and Abstract Algebra enthusiasts.

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