Timeline for Arithmetic progressions inside polynomial sets
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
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| Jul 13, 2012 at 12:21 | answer | added | Eduardo Jose | timeline score: -2 | |
| Oct 1, 2011 at 17:09 | answer | added | Noam D. Elkies | timeline score: 4 | |
| Oct 1, 2011 at 11:05 | answer | added | Eduardo José | timeline score: 0 | |
| Mar 26, 2011 at 19:30 | history | edited | Charles |
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| Mar 26, 2011 at 18:09 | history | edited | Manuel Silva | CC BY-SA 2.5 |
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| Mar 25, 2011 at 20:05 | comment | added | Manuel Silva | @Mark: The points do not have to be on a straight line. Take for example (1,1), (5,25) and (7, 49) which correspond to the 3-AP of squares 1, 25, 49. | |
| Mar 25, 2011 at 20:02 | comment | added | Thomas Bloom | This doesn't help with your problem, but it is interesting to note that as soon as we allow two variables, we get arbitrarily long arithmetic progressions from only a quadratic example: the polynomial $x^2+y^2$, for example. This is an immediate consequence of the Green-Tao theorem. | |
| Mar 25, 2011 at 19:08 | comment | added | Mark Bennet | Don't terms in arithmetic progression lie on a straight line, and we are talking about the intersection of a polynomial with a straight line? | |
| Mar 25, 2011 at 17:35 | history | edited | Manuel Silva | CC BY-SA 2.5 |
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| Mar 25, 2011 at 0:40 | history | edited | Manuel Silva | CC BY-SA 2.5 |
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| Mar 24, 2011 at 23:39 | answer | added | Gerry Myerson | timeline score: 1 | |
| Mar 24, 2011 at 22:23 | history | edited | Manuel Silva | CC BY-SA 2.5 |
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| Mar 24, 2011 at 21:50 | comment | added | Kevin Buzzard | If there was no uniform bound for $f(A_p)$ for degree three polynomials, then (after scaling etc) I could find a cubic $f(x)$ and rationals $x_1$, $x_2$, $x_3$...$x_{1000000}$ such that $f(x_n)=n$. Now because 1000 of these $n$ are squares I have now got 1000 points on $y^2=f(x)$ and now perhaps I am pretty close to constructing elliptic curves with arbitrarily large rank. It's unclear to me what the concensus is about these things existing. Similarly I can construct curves of genus 3, say, over Q with as many points as you like and again it's not clear that such things should exist. | |
| Mar 24, 2011 at 20:33 | history | asked | Manuel Silva | CC BY-SA 2.5 |