20090913, 18:30  #1  
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Aug 2009
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Congruence
Quote:


20090913, 18:57  #2 
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"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
Here's my understanding of it, simple as can be: (for modular arithmetic, at least) 13 is congruent to 1 modulo 12 because each are one higher than a multiple of 12. Or in formula form:
Where means congruent to. 
20090913, 21:28  #3 
Aug 2004
Melbourne, Australia
152_{10} Posts 
``Congruence'' means ``equivalence'' in some sense. This is one of the words in mathematics that has many meanings depending on what area of mathematics your interested in (eg. there are congruent triangles also).
Typically in number theory... two integers are congruent modulo m if they have the same remainder after division by m. In MiniGeek's example m=12. We see that 13 after division by 12 leaves a remainder 1. Similarly, 1 after division by 12 also leaves a remainder 1. In fact, all of the numbers in are congruent modulo 12. This can also be extended to negative integers too, so are all congruent modulo 12. 
20090913, 21:56  #4  
Jul 2006
Calgary
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Quote:
IANAM so YMMV 

20090913, 23:16  #5  
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The reason I ask is I was trying to understand what is below:
Quote:
Last fiddled with by storm5510 on 20090914 at 00:05 

20090914, 00:48  #6  
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"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
In other words:
Quote:
Quote:
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(I'll assume you understand the rest of it, like the 'for' loop) http://en.wikipedia.org/wiki/Miller%...primality_test has explanations, pseudocode, an example, etc. Last fiddled with by MiniGeek on 20090914 at 00:52 

20090914, 01:34  #7 
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I wasn't much concerned with the rest. Just the term. I rather doubt something like this could be coded, reliably anyway.
Thanks. 
20090914, 02:49  #8 
"Ben"
Feb 2007
6556_{8} Posts 

20090914, 02:51  #9 
Jul 2006
Calgary
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20090914, 16:02  #10  
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Quote:
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20090914, 18:33  #11 
Nov 2003
2^{2}×5×373 Posts 

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