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#463 |
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Jan 2010
379 Posts |
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#464 | |
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Nov 2003
22·5·373 Posts |
Quote:
e.g. let m = 8. The units are 1,3,5,7. Their product mod 8 is 7. This clearly isn't 1. let m = 10, the units are 1,3,7,9. Their product mod 10 is 9. This clearly isn't 1. |
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#465 |
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Jan 2010
379 Posts |
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#466 |
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Nov 2003
22×5×373 Posts |
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#467 | |
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Jan 2010
379 Posts |
Quote:
For evey m with a residue class m-1, a=m-1. Example: m=16. 3*5=b(mod 16) b=3*5=16-1. And further more: d(m)=a(mod 16) a=16-1. Where b is the residue class of (3,5). Last fiddled with by blob100 on 2010-06-02 at 16:46 |
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#468 | |
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Nov 2003
22·5·373 Posts |
Quote:
(1) You need to justify your answer. How did you get it? Show your work. It is not sufficient to simply assert the answer. (2) You need to determine which m give the answer 1, and which m give the answer -1. Hint: This is closely related to a problem we already looked at. Think about the units that are their own inverse. |
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#469 | |
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Aug 2005
Seattle, WA
175410 Posts |
Quote:
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#470 |
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Nov 2003
1D2416 Posts |
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#471 | |
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May 2010
Prime hunting commission.
24·3·5·7 Posts |
Quote:
Last fiddled with by 3.14159 on 2010-06-02 at 23:43 |
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#472 |
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Dec 2008
72·17 Posts |
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#473 | |
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May 2010
Prime hunting commission.
24·3·5·7 Posts |
Quote:
Proofs: 431/2 =/= Integer 431/3 =/= Integer 431/5 =/= Integer 431/7 =/= Integer 431/11 =/= Integer 431/13 =/= Integer 431/17 =/= Integer 431/19 = Integer sqrt(431) = 20 431 is prime QED Last fiddled with by 3.14159 on 2010-06-02 at 23:51 |
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