Timeline for Subset of the integers with certain properties
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2014 at 1:42 | vote | accept | Mayank Pandey | ||
| Sep 7, 2014 at 1:40 | vote | accept | Mayank Pandey | ||
| Sep 7, 2014 at 1:40 | |||||
| Aug 12, 2014 at 12:43 | answer | added | Jan-Christoph Schlage-Puchta | timeline score: 4 | |
| Jul 26, 2014 at 3:38 | comment | added | Brendan McKay | All but at most two of the integers is a multiple of 4. Don't know if that helps. | |
| Jul 25, 2014 at 9:12 | history | edited | Asaf Karagila♦ |
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| Jul 25, 2014 at 9:06 | comment | added | Włodzimierz Holsztyński | I'd consider first two related questions: what is the largest $n$ for which there exists an $n$-set $S \subseteq \{1\ 2\ \ldots\}$ such that for every $A\subseteq S$ the sum $\sum_{a\in A}\ a^2$ is a square or a third power; and for the other question replace $a^2$ by $a^3$, and otherwise the question would look the same. Indeed, when a set of squares and cubes is large than the set of its squares or its cubes is at least half that large. | |
| Jul 25, 2014 at 7:41 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
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| Jul 25, 2014 at 3:19 | comment | added | Gerry Myerson | If you can find a set of 3 non-zero integers such that all subsets sum to squares, you will have solved the notorious integer cuboid problem. | |
| Jul 25, 2014 at 3:05 | comment | added | The Masked Avenger | Of course, I then think of S being the first 5 positive integers. Very well, let's say one-half to be safe. | |
| Jul 25, 2014 at 2:59 | comment | added | The Masked Avenger | I think it is unknown that for S with, say 5 or more elements, that at least a third of it subsets add up to perfect powers or even squarefull numbers with common gcd 1. I have no references to support this more general assertion. | |
| Jul 25, 2014 at 2:40 | history | asked | Mayank Pandey | CC BY-SA 3.0 |