20101207, 14:47  #1 
"Forget I exist"
Jul 2009
Dumbassville
2^{3}×1,049 Posts 
modular arithmetic
I was wondering how much I knew about modular arithmetic and if anyone else could add more it would be appreciated. I know (a*b) mod x = (a mod x * b mod x)mod x, I've thought about addition and a few others as well looks like it holds for other operations. I know there's more than this to modular arithmetic anyone care to expand my knowledge or give me a link because they don't care lol I can look up more I guess I will have to.

20101207, 15:34  #2 
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
Your post count is approaching that of the legendary Mally, sm.

20101207, 15:46  #3 
"Forget I exist"
Jul 2009
Dumbassville
2^{3}×1,049 Posts 

20101207, 18:49  #4 
Aug 2006
13535_{8} Posts 
For basic introductions, see
http://www.cuttheknot.org/blue/Modulo.shtml http://www.math.rutgers.edu/~erowlan...rithmetic.html For more depth, I suggest finding a basic number theory textbook, maybe at a local library. Alternately, here are some online texts: http://www.math.usf.edu/~eclark/elem_num_th_book.pdf http://shoup.net/ntb/ http://modular.math.washington.edu/ent/ 
20101207, 19:06  #5 
"Lucan"
Dec 2006
England
2·3·13·83 Posts 

20101207, 22:29  #6  
"Forget I exist"
Jul 2009
Dumbassville
2^{3}·1,049 Posts 
Quote:


20101207, 22:30  #7 
May 2010
Prime hunting commission.
2^{4}×3×5×7 Posts 
Operations using modular arithmetic;
(a mod x + b mod x) mod x = (a + b) mod x. (a mod x * b mod x) mod x = (a * b) mod x. The above does not hold for exponentiation; ((261 mod 19)↑(771 mod 19)) mod 19 != (261↑771) mod 19. Last fiddled with by 3.14159 on 20101207 at 22:34 
20101207, 22:42  #8  
Aug 2006
175D_{16} Posts 
Quote:


20101207, 22:46  #9 
Aug 2006
13535_{8} Posts 

20101208, 00:20  #10 
May 2010
Prime hunting commission.
1680_{10} Posts 

20101208, 00:25  #11 
May 2010
Prime hunting commission.
690_{16} Posts 
Going back to my example: By phi, do you mean, phi(19, (exponent))? Or do you mean, 19?
Last fiddled with by 3.14159 on 20101208 at 00:26 
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