Timeline for Quadratic Diophantine equations with all values prime
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2021 at 22:13 | comment | added | Stanley Yao Xiao | Even in the simplest cases this type of question is almost impossible to answer. For example, suppose we are looking at the equation $x^2 - 2y^2 = \pm 1$. The solutions are generated by $1 + \sqrt{2}$, by looking at the rational/irrational parts of $(1 + \sqrt{2})^n$. The rational parts are given by $\sum_{j=0}^{\lfloor n/2 \rfloor} \binom{n}{2j} 2^j$. Asking whether this is prime infinitely often is already well-beyond what we know how to do: we can't even answer this question for the easier looking sequence $2^k - 1$ (the Mersenne sequence). | |
| Feb 7, 2021 at 21:54 | answer | added | Will Jagy | timeline score: 2 | |
| Feb 7, 2021 at 21:06 | history | edited | JoshuaZ | CC BY-SA 4.0 |
correct initial equation and add parenthetical note.
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| Feb 7, 2021 at 21:05 | comment | added | JoshuaZ | @WillJagy Ah yes, there should be an $f$ term in the original. Good catch. | |
| Feb 7, 2021 at 20:58 | comment | added | Will Jagy | for p,q to be the variables, your general quadratic needs to have a constant term $f$ to accommodate the $ma^2$ | |
| S Feb 7, 2021 at 20:20 | history | suggested | gmvh |
Added top-level tag
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| Feb 7, 2021 at 20:11 | review | Suggested edits | |||
| S Feb 7, 2021 at 20:20 | |||||
| Feb 7, 2021 at 20:05 | history | edited | JoshuaZ | CC BY-SA 4.0 |
delete redundant word
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| Feb 7, 2021 at 18:05 | history | edited | JoshuaZ | CC BY-SA 4.0 |
fix right to left, and expand sum note
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| Feb 7, 2021 at 18:03 | comment | added | JoshuaZ | @dodd Sorry, that should be the left hand side. | |
| S Feb 7, 2021 at 18:03 | history | suggested | markvs | CC BY-SA 4.0 |
Fixed misprint in the title
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| Feb 7, 2021 at 18:03 | comment | added | markvs | "barring the exceptional case where the right-hand side itself factors"? The RHS is $0$. | |
| Feb 7, 2021 at 18:02 | review | Suggested edits | |||
| S Feb 7, 2021 at 18:03 | |||||
| Feb 7, 2021 at 17:41 | history | asked | JoshuaZ | CC BY-SA 4.0 |