Timeline for Conditions to the existence of a solution of a system of congruences [closed]
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 29, 2011 at 6:46 | history | closed |
user6976 Felipe Voloch Andreas Blass David Loeffler Andrés E. Caicedo |
too localized | |
| Sep 28, 2011 at 15:59 | comment | added | David Loeffler | @Carl: Watch your logical connectives! The question you just asked is totally vacuous. I think you meant "... only if there exists one to the whole system". Here the answer is (almost as obviously) no: consider the equations $x+y=1, x=0, y=0$ -- any two of these are simultaneously solvable but the three are obviously not simultaneously solvable. But to reiterate what others have already said, with coefficients in $\mathbb{R}$ these would be totally trivial undergraduate linear algebra exercises, and linear algebra over $\mathbb{F}_p$ works just the same. | |
| Sep 28, 2011 at 13:44 | comment | added | Carl | For example, is it true that there exists a solution to each pair of congruences if there exists one to the whole system? | |
| Sep 28, 2011 at 13:40 | comment | added | Igor Rivin | You only have one prime -- you can't get much more local than that. | |
| Sep 28, 2011 at 13:27 | comment | added | Carl | That's not what I'm looking for. I'm looking for local conditions as in the case of proofwiki.org/wiki/Solution_to_Simultaneous_Linear_Congruences | |
| Sep 28, 2011 at 12:50 | comment | added | Martin Bright | Carl - this question will probably get closed soon since it is more appropriate for math.stackexchange.com. However, two comments: (1) What are the conditions for such a system of equations to be soluble over the real numbers? If you can't answer this, you should read up on linear algebra first. (2) The integers modulo p form a field, so pretty much everything you know about linear algebra over the reals works mod p without any changes. | |
| Sep 28, 2011 at 12:48 | answer | added | Igor Rivin | timeline score: 2 | |
| Sep 28, 2011 at 12:47 | history | edited | Carl | CC BY-SA 3.0 |
added 129 characters in body
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| Sep 28, 2011 at 12:42 | history | asked | Carl | CC BY-SA 3.0 |