Timeline for Analysis of a quadratic diophantine equation
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2010 at 19:57 | answer | added | John R Ramsden | timeline score: 4 | |
| Oct 30, 2010 at 16:49 | history | edited | Franz Lemmermeyer |
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| Oct 30, 2010 at 16:48 | answer | added | Franz Lemmermeyer | timeline score: 8 | |
| Oct 28, 2010 at 9:00 | comment | added | Franz Lemmermeyer | Following the line of attack outlined in my answer (now deleted because it got downvoted so often) I have found several parametrized families on the surface; one of them is given by $(X,Y,Z,W) = (16u^5 + 16u^3 + 5u, 16u^4+12u^2+1, 16u^5 + 24u^3 + 7u, 16u^5 + 8u^3 - u). $ I have found infinitely many integral solutions of the original equation, though none yet in which a, b, c, d are all positive. | |
| Oct 25, 2010 at 23:28 | comment | added | Gerry Myerson | An earlier reference to this problem is on page 217 of Rabinowitz and Bowron, Index to Mathematical Problems, 1975-1979. It's attributed to Robert A Carman, School Science and Mathematics problem 3589. | |
| Oct 25, 2010 at 23:22 | comment | added | Gerry Myerson | Finding the smallest example was Project Euler: Problem 44, see projecteuler.net/index.php?section=problems&id=44 | |
| Oct 25, 2010 at 22:49 | vote | accept | apples | ||
| Oct 25, 2010 at 20:59 | answer | added | David Lehavi | timeline score: 3 | |
| Oct 25, 2010 at 20:43 | answer | added | rita the dog | timeline score: 0 | |
| Oct 25, 2010 at 20:43 | comment | added | Kevin Buzzard | [indeed I sort-of suspect that one will be able to write down an infinite family of solutions, by first finding a rational pamaterisation of the intersection and then looking for integer points on it, but that it will take some work...] | |
| Oct 25, 2010 at 20:38 | comment | added | Kevin Buzzard | Diophantine equations like this can be very tough. Elementary algebraic manipulations often get you nowhere (there is sometimes a trick but often not). Do you have any reason to believe the solutions to this equation are "nice" in any way? Here's one for your enjoyment: a=2167;b=1020;c=2395;d=1912 (if my computer got it right...) and I sort-of suspect there will be a sparse but infinite set of solutions. | |
| Oct 25, 2010 at 6:59 | answer | added | Robin Chapman | timeline score: 5 | |
| Oct 25, 2010 at 6:48 | history | asked | apples | CC BY-SA 2.5 |