Timeline for Probability of all combinations of k numbers among n being coprime
Current License: CC BY-SA 3.0
6 events
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| Jan 25, 2013 at 1:19 | comment | added | Greg Martin | Indeed, Toth seems to have proved this statement (about $n$ randomly chosen integers being pairwise coprime) in a 2002 Fibonacci Quarterly paper. ams.org/mathscinet-getitem?mr=1885265 | |
| Jan 22, 2013 at 1:28 | comment | added | Greg Martin | The formula in the answer certainly reduces, when $k=2$ (pairwise coprime), to $\prod_q (1-q^{-1})^{n-1}(1+(n-1)q^{-1})$, validating Finch's statement. | |
| Jan 21, 2013 at 2:11 | comment | added | Alex G | Nice. Even though as you might have guessed, I was hoping for an answer involving the zeta function. | |
| Jan 21, 2013 at 2:09 | vote | accept | Alex G | ||
| Jan 20, 2013 at 22:13 | comment | added | Gerry Myerson | This .286747... is also the probability that two positive integers are "strongly carefree," that is, coprime and both squarefree, see Finch, Mathematical Constants, p. 110. Next page, Finch notes the probability $k$ integers are pairwise coprime is $\prod(1-p^{-1})^{k-1}(1+(k-1)p^{-1})$ for $k=2,3$, unproved for $k\gt3$. Some of Finch's references are to unpublished work of Moree. A published reference is Schroeder's book, Number Theory in Science and Communication, pp 25, 48-51, and 54. | |
| Jan 20, 2013 at 20:13 | history | answered | Greg Martin | CC BY-SA 3.0 |