Timeline for Mathematical induction vis-à-vis primes
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
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| 4 hours ago | history | edited | LSpice | CC BY-SA 4.0 |
vis-a-vis -> vis-à-vis
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| 7 hours ago | history | edited | mathoverflowUser |
added tag number-theory
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| 12 hours ago | answer | added | mathoverflowUser | timeline score: 0 | |
| Jun 19, 2017 at 2:35 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jun 18, 2017 at 3:03 | review | Close votes | |||
| Jun 19, 2017 at 1:11 | |||||
| Jun 14, 2017 at 7:13 | answer | added | José Hdz. Stgo. | timeline score: 2 | |
| Jun 12, 2017 at 15:11 | history | edited | T. Amdeberhan | CC BY-SA 3.0 |
deleted 8 characters in body
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| Jun 12, 2017 at 15:05 | comment | added | T. Amdeberhan | That is exactly what I meant to say. | |
| Jun 12, 2017 at 15:04 | comment | added | user39297 | Do you mean induction that is taken over the primes? | |
| Jun 12, 2017 at 14:58 | history | edited | T. Amdeberhan | CC BY-SA 3.0 |
added 195 characters in body
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| Jun 12, 2017 at 9:13 | comment | added | Dirk | Are you specifically looking for inductions going from $p_n$ to $p_{n+1}$, or would something like "Assume the statement is true for all $p_i$ with $i \leq n$. Show that it is true for $p_n$." also work? Because I think there are far more examples for the latter case. | |
| Jun 12, 2017 at 8:28 | comment | added | KConrad | Another example is in the work on Serre's conjecture by Khare and Wintenberger. See the bottom of page 25 of arxiv.org/pdf/math/0412076.pdf. | |
| Jun 12, 2017 at 8:20 | comment | added | KConrad | What is the motivation for this question: idle curiosity? In any case, the first proof of quadratic reciprocity by Gauss was an induction on the primes. Tate used that "ugly" proof in his calculation of $K_2(\mathbf Q)$, which is also an induction on primes (see Rosenberg's textbook on $K$-theory). | |
| Jun 12, 2017 at 7:00 | answer | added | Anthony Quas | timeline score: 1 | |
| Jun 12, 2017 at 6:42 | answer | added | Wlod AA | timeline score: 2 | |
| Jun 12, 2017 at 4:57 | comment | added | Arturo Magidin | Not quite going through the regular sequence of primes in the usual order, but Baumslag proved that a finitely generated nilpotent group can be embedded in a locally nilpotent radicable group by taking a sequence of primes $p_1,p_2,\ldots,$ with the property that for all primes $p$ and all positive integers $m$, there exists an $n\gt m$ such that $p=p_n$ (so each prime occurs infinitely many times); and then adjoining $p_n$th roots to all elements already constructed to get the "next" group. | |
| Jun 12, 2017 at 4:53 | review | Close votes | |||
| Jun 12, 2017 at 11:53 | |||||
| Jun 12, 2017 at 4:30 | comment | added | Gerhard Paseman | Or like mathoverflow.net/q/160403 ? Gerhard "Still Not Sure About This" Paseman, 2017.06.11. | |
| Jun 12, 2017 at 4:21 | comment | added | Wojowu | Something like this? | |
| Jun 12, 2017 at 4:06 | comment | added | T. Amdeberhan | You're right, I added a sentence to clarify a little bit. | |
| Jun 12, 2017 at 4:05 | history | edited | T. Amdeberhan | CC BY-SA 3.0 |
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| Jun 12, 2017 at 3:51 | comment | added | Gerhard Paseman | Fundamental theorem of arithmetic? Various statements on finite groups? Euclid's proof rearranged? What form of induction do you want? Gerhard "Can You Be More Specific?" Paseman, 2017.06.11. | |
| Jun 12, 2017 at 3:24 | history | asked | T. Amdeberhan | CC BY-SA 3.0 |