MHB Possibility of a Separate Forum for NT & Abstract Algebra

AI Thread Summary
The discussion advocates for the creation of separate forums for Number Theory (NT) and Abstract Algebra. Participants are exploring a mathematical problem involving the demonstration of infinitely many integers n such that both 6n + 1 and 6n - 1 are composite. One contributor proposes using n = 35x - 1 to derive the expressions for 6n + 1 and 6n - 1, successfully showing their composite nature. Another participant suggests an alternative approach with n = 36k^3, indicating a connection to the sum and difference of cubes. The conversation highlights both the need for specialized forums and ongoing mathematical exploration.
The Chaz
Messages
206
Reaction score
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.
 
Mathematics news on Phys.org
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
 
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...
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

Insights Fermat's Last Theorem
3
Replies
105
Views
6K
I Proving inequality about dimension of quotient vector spaces
Replies
25
Views
3K
Courses Is proof based Linear Algebra be similar to Abstract Algebra
Replies
6
Views
5K
MHB Solving Nilpotent Problem in Abstract Algebra
Replies
3
Views
2K
Algebra Seeking Recommendation on Abstract Algebra textbooks
Replies
7
Views
4K
  • Sticky
Other Collection of Free Online Math Books and Lecture Notes (part 1)
Replies
16
Views
10K
Solutions to Hungerford's "Abstract Algebra" 3rd Ed.
Replies
4
Views
4K
Programs Possible double major: abstract algebra or otherwise?
Replies
2
Views
1K
Challenge Math Challenge Thread (October 2023)
Replies
25
Views
4K
Links between sub-fields of mathematics
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top