Timeline for Not especially famous, long-open problems which anyone can understand
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2023 at 2:26 | comment | added | Timothy Chow | Related MO question: Singmaster's conjecture | |
| Nov 9, 2022 at 11:29 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Jul 20, 2021 at 8:51 | comment | added | Archie | The conjecture has been proved in a large interior region in this paper by 5 coauthors arxiv.org/abs/2106.03335 | |
| Mar 31, 2021 at 0:59 | comment | added | Timothy Chow | Here's a link to the other MO question that you alluded to. | |
| Dec 3, 2020 at 1:15 | comment | added | Benjamin Wang | A bit late to the party, but you might be interested in that Singmaster's Conjecture appeared on a Matt Parker video: youtu.be/tjJ2qL9uaz4 Timestamp 3:14 :) | |
| Oct 17, 2017 at 3:26 | comment | added | Michael Hardy | @FranciscoSantos : Certainly $\dbinom {2k} k$ appears an add number of times and that odd number is at least three. But it's been proved that infinitely many appear exactly three times. | |
| Oct 17, 2017 at 1:07 | comment | added | Francisco Santos | "It has been proved that infinitely many numbers appear twice; similarly three times, four times". I guess most of this is easy: every prime number $p$ appears exactly twice, every number of the form $\binom{p}{2}$ ($p\ge 5$) appears exactly four times, and every number of the form $\binom{2k}{k}$ appears an odd and at least three number of times. | |
| Oct 31, 2016 at 6:26 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
deleted 1 character in body
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| Apr 15, 2013 at 10:39 | history | edited | user112109 | CC BY-SA 3.0 |
added 1 characters in body
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| Jul 22, 2012 at 18:44 | comment | added | Vectornaut | I love this problem! Everything about it is simple and compelling, and it can be understood by anyone who knows how to add. Is there also a simple heuristic argument for why it should be true? @S. Carnahan , can you flesh out your heuristics a little more? What's this stuff about geometry of plane curves? | |
| Jul 12, 2012 at 7:02 | comment | added | S. Carnahan♦ | Odd multiplicity means you have a number of the form $\binom{2k}{k}$. It's not hard to check whether a number has the form of a binomial coefficient $\binom{m}{n}$ in SAGE, since you have a built-in function that estimates integer $n$-th roots. | |
| Jul 6, 2012 at 21:49 | comment | added | Michael Hardy | @S.Carnahan : How did you do that "short computation"? | |
| Jul 2, 2012 at 9:49 | comment | added | S. Carnahan♦ | We don't really need Erdős to tell us it's probably true when we can do straightforward probabilistic estimates (plus some geometry of plane curves). A short computation shows that there are no numbers less than $10^{1000}$ that have odd multiplicity greater than 3, and heuristics suggest it is quite unlikely that such numbers exist. | |
| Jul 1, 2012 at 19:48 | history | answered | Michael Hardy | CC BY-SA 3.0 |