Timeline for Covering Systems of infinite sets of residue classes mod primes
Current License: CC BY-SA 3.0
20 events
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| Nov 19, 2016 at 21:12 | history | edited | Gerry Myerson | CC BY-SA 3.0 |
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| Nov 19, 2016 at 16:15 | comment | added | JustKevin | {1} isn't in the covering if each residue is 0. However, I will expound below. | |
| Jul 29, 2011 at 20:59 | history | edited | Charles |
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| Jan 18, 2011 at 18:09 | history | edited | Asterios Gkantzounis | CC BY-SA 2.5 |
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| Jan 18, 2011 at 15:33 | history | edited | Charles |
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| Jan 18, 2011 at 12:44 | history | edited | Asterios Gkantzounis | CC BY-SA 2.5 |
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| Jan 15, 2011 at 17:26 | history | edited | Asterios Gkantzounis | CC BY-SA 2.5 |
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| Jan 15, 2011 at 17:08 | history | edited | Asterios Gkantzounis | CC BY-SA 2.5 |
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| Jan 15, 2011 at 14:42 | history | edited | Asterios Gkantzounis | CC BY-SA 2.5 |
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| Jan 15, 2011 at 12:47 | history | edited | Asterios Gkantzounis | CC BY-SA 2.5 |
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| Jan 15, 2011 at 12:42 | comment | added | Mark Bennet | Asterios - it is hard to see what your precise question is. How "given" is your set of primes/set of residues - can you choose either? Do you expect either to have any regularity because of how they arise? | |
| Jan 15, 2011 at 12:22 | comment | added | Asterios Gkantzounis | Wadim :The criteria could be about the density of the residue classes as Aaron wrote or other do you have any? | |
| Jan 15, 2011 at 12:15 | comment | added | Wadim Zudilin | It's pulling the wool over MO's eyes. | |
| Jan 15, 2011 at 12:13 | comment | added | Asterios Gkantzounis | I asked for known results on this direction | |
| Jan 15, 2011 at 12:07 | comment | added | Wadim Zudilin | I needed more than 10 minutes just to understand your question! ;-) I'll definitely state it simpler and shorter. But I would need more time ($\infty$?) to understand what's use of all this. What kind of criteria do you expect? Pick a number $n\in\mathbb N$, check whether it belongs to a certain residue class. If yes, take $n+1$, and so on. There can't be a finite procedure to answer your Q. | |
| Jan 15, 2011 at 12:04 | comment | added | Mark Bennet | If you choose residue zero for all the primes in your set then there is an infinite set of integers you don't hit (multiples of all the other primes). If p is your smallest prime, then you need 1, 2 ... (p-1) as explicit residue classes. I think also that if the sum of the reciprocals of your infinite set is infinite, a random selection of residue classes will almost certainly hit each integer (uniform for each prime). It is easy to construct sets of residues which miss any finite set of numbers with cardinality less than the smallest prime (smallest residue which misses for each prime). | |
| Jan 15, 2011 at 11:51 | comment | added | Asterios Gkantzounis | What do you mean there are not such covering systems at all ,for trivial reasoning .Is there something that is not well written?Or else please give the trivial reasoning. | |
| Jan 15, 2011 at 11:50 | comment | added | Wadim Zudilin | If you know how to pick the infinite set of primes, you are infinitely rich. :-) Jokes aside, your question isn't formulated well. Vote to close. | |
| Jan 15, 2011 at 11:23 | answer | added | Aaron Meyerowitz | timeline score: 2 | |
| Jan 15, 2011 at 11:09 | history | asked | Asterios Gkantzounis | CC BY-SA 2.5 |