simple hyperbolic Diophantine equation [on hold]

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
1
down vote

favorite












How can we show that there are infinitely many integers $C$ such that the simple hyperbolic diophantine equation:
$$6xy ± x ± y = C$$ gives a non-integer solutions for $x, y$, except at $(0, ±C), (±C,0)$?



Some of these values of $C = 3,5,7,10,…$.




diophantine-equations




share|cite|improve this question













put on hold as off-topic by Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, Taroccoesbrocco 5 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, Taroccoesbrocco
If this question can be reworded to fit the rules in the help center, please edit the question.












  • math.stackexchange.com/questions/2496106/… and math.stackexchange.com/questions/2324324/… and math.stackexchange.com/questions/550916/… and math.stackexchange.com/questions/1416570/… and math.stackexchange.com/questions/698021/…
    – Gerry Myerson
    yesterday














up vote
1
down vote

favorite












How can we show that there are infinitely many integers $C$ such that the simple hyperbolic diophantine equation:
$$6xy ± x ± y = C$$ gives a non-integer solutions for $x, y$, except at $(0, ±C), (±C,0)$?



Some of these values of $C = 3,5,7,10,…$.




diophantine-equations




share|cite|improve this question













put on hold as off-topic by Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, Taroccoesbrocco 5 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, Taroccoesbrocco
If this question can be reworded to fit the rules in the help center, please edit the question.












  • math.stackexchange.com/questions/2496106/… and math.stackexchange.com/questions/2324324/… and math.stackexchange.com/questions/550916/… and math.stackexchange.com/questions/1416570/… and math.stackexchange.com/questions/698021/…
    – Gerry Myerson
    yesterday












up vote
1
down vote

favorite









up vote
1
down vote

favorite











How can we show that there are infinitely many integers $C$ such that the simple hyperbolic diophantine equation:
$$6xy ± x ± y = C$$ gives a non-integer solutions for $x, y$, except at $(0, ±C), (±C,0)$?



Some of these values of $C = 3,5,7,10,…$.




diophantine-equations




share|cite|improve this question













How can we show that there are infinitely many integers $C$ such that the simple hyperbolic diophantine equation:
$$6xy ± x ± y = C$$ gives a non-integer solutions for $x, y$, except at $(0, ±C), (±C,0)$?



Some of these values of $C = 3,5,7,10,…$.





diophantine-equations





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited yesterday









Suzet

2,023324




2,023324









asked yesterday









busy Ang

183




183




put on hold as off-topic by Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, Taroccoesbrocco 5 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, Taroccoesbrocco
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, Taroccoesbrocco 5 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Jendrik Stelzner, Brahadeesh, José Carlos Santos, Taroccoesbrocco
If this question can be reworded to fit the rules in the help center, please edit the question.











  • math.stackexchange.com/questions/2496106/… and math.stackexchange.com/questions/2324324/… and math.stackexchange.com/questions/550916/… and math.stackexchange.com/questions/1416570/… and math.stackexchange.com/questions/698021/…
    – Gerry Myerson
    yesterday
















  • math.stackexchange.com/questions/2496106/… and math.stackexchange.com/questions/2324324/… and math.stackexchange.com/questions/550916/… and math.stackexchange.com/questions/1416570/… and math.stackexchange.com/questions/698021/…
    – Gerry Myerson
    yesterday















math.stackexchange.com/questions/2496106/… and math.stackexchange.com/questions/2324324/… and math.stackexchange.com/questions/550916/… and math.stackexchange.com/questions/1416570/… and math.stackexchange.com/questions/698021/…
– Gerry Myerson
yesterday




math.stackexchange.com/questions/2496106/… and math.stackexchange.com/questions/2324324/… and math.stackexchange.com/questions/550916/… and math.stackexchange.com/questions/1416570/… and math.stackexchange.com/questions/698021/…
– Gerry Myerson
yesterday










1 Answer
1






active

oldest

votes

















up vote
1
down vote



accepted










This is OEIS sequence A002822 "Numbers n such that 6n-1, 6n+1 are twin primes". Thus, proving there are infinitely many of these numbers is equivalent to proving the twin prime conjecture.






share|cite|improve this answer























  • thank you very much for the feedback.
    – busy Ang
    yesterday

















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










This is OEIS sequence A002822 "Numbers n such that 6n-1, 6n+1 are twin primes". Thus, proving there are infinitely many of these numbers is equivalent to proving the twin prime conjecture.






share|cite|improve this answer























  • thank you very much for the feedback.
    – busy Ang
    yesterday














up vote
1
down vote



accepted










This is OEIS sequence A002822 "Numbers n such that 6n-1, 6n+1 are twin primes". Thus, proving there are infinitely many of these numbers is equivalent to proving the twin prime conjecture.






share|cite|improve this answer























  • thank you very much for the feedback.
    – busy Ang
    yesterday












up vote
1
down vote



accepted







up vote
1
down vote



accepted






This is OEIS sequence A002822 "Numbers n such that 6n-1, 6n+1 are twin primes". Thus, proving there are infinitely many of these numbers is equivalent to proving the twin prime conjecture.






share|cite|improve this answer















This is OEIS sequence A002822 "Numbers n such that 6n-1, 6n+1 are twin primes". Thus, proving there are infinitely many of these numbers is equivalent to proving the twin prime conjecture.







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited yesterday


























answered yesterday









Somos

10.8k1831




10.8k1831











  • thank you very much for the feedback.
    – busy Ang
    yesterday
















  • thank you very much for the feedback.
    – busy Ang
    yesterday















thank you very much for the feedback.
– busy Ang
yesterday




thank you very much for the feedback.
– busy Ang
yesterday


Comments

Post a Comment

Popular posts from this blog

What is the equation of a 3D cone with generalised tilt?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an...
Read more

Color the edges and diagonals of a regular polygon

Image
Clash Royale CLAN TAG #URR8PPP up vote 5 down vote favorite 1 Here is the problem: For what $n$ is it possible to color the edges and diagonals of an $n$-side regular polygon with $dfracbinomn23$ colors, such that you use every color exactly three times and for every color the three segments (edges or diagonals) with that color form a triangle? Trivially $nequiv 0 text or 1 pmod3$. I can also prove that if the statement is true for $k$ than it is true for $3k$ as well. How to finish? Please help! Thanks combinatorial-geometry share | cite | improve this question edited Aug 6 at 21:57 alcana 118 4 asked Aug 6 at 21:15 Leo Gardner 356 11 Even assuming "polyhpn" in the title is a typo for polygon , it is unclear what you mean by "the edges and sides". Aren't the side of a regular polygon the same as the edges? A regular $n$-sided polygon has $n$ edges. – hardmath Aug 6 at 21:20 3 $n$ ne...
Read more

Relationship between determinant of matrix and determinant of adjoint?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). – Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/…...
Read more