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.

Your post count is approaching that of the legendary Mally, sm.

[QUOTE=davieddy;240513]Your post count is approaching that of the legendary Mally, sm.[/QUOTE]
so in other words I should stop ? 
For basic introductions, see
[url]http://www.cuttheknot.org/blue/Modulo.shtml[/url] [url]http://www.math.rutgers.edu/~erowland/modulararithmetic.html[/url] For more depth, I suggest finding a basic number theory textbook, maybe at a local library. Alternately, here are some online texts: [url]http://www.math.usf.edu/~eclark/elem_num_th_book.pdf[/url] [url]http://shoup.net/ntb/[/url] [url]http://modular.math.washington.edu/ent/[/url] 
[QUOTE=science_man_88;240515]so in other words I should stop ?[/QUOTE]
Nah. Hasn't done me any harm. Yet. Touch wood. David 
[QUOTE=CRGreathouse;240540]For basic introductions, see
[url]http://www.cuttheknot.org/blue/Modulo.shtml[/url] [url]http://www.math.rutgers.edu/~erowland/modulararithmetic.html[/url] For more depth, I suggest finding a basic number theory textbook, maybe at a local library. Alternately, here are some online texts: [url]http://www.math.usf.edu/~eclark/elem_num_th_book.pdf[/url] [url]http://shoup.net/ntb/[/url] [url]http://modular.math.washington.edu/ent/[/url][/QUOTE] I see uses I never thought of as modular arithmetic lol. 
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 [B]not[/B] hold for exponentiation; ((261 mod 19)↑(771 mod 19)) mod 19 != (261↑771) mod 19. 
[QUOTE=science_man_88;240508]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.[/QUOTE]
[QUOTE=3.14159;240571]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.[/QUOTE] Yes. But it's sometimes useful to reduce only partially: (a  Ax)(b  Bx) mod x = a * b mod x. This is used in some efficient algorithms where fully reducing at each step would be more costly. 
[QUOTE=3.14159;240571]The above does [B]not[/B] hold for exponentiation;
((261 mod 19)↑(771 mod 19)) mod 19 != (261↑771) mod 19.[/QUOTE] Right. The base can be reduced mod the exponent, and the exponent can... usually... be reduced mod phi(the modulus). 
[QUOTE=CRGreathouse;240575]Yes. But it's sometimes useful to reduce only partially: (a  Ax)(b  Bx) mod x = a * b mod x. This is used in some efficient algorithms where fully reducing at each step would be more costly.[/QUOTE]
List a few examples. 
[QUOTE=CRGreathouse;240577]Right. The base can be reduced mod the exponent, and the exponent can... usually... be reduced mod phi(the modulus).[/QUOTE]
Going back to my example: By phi, do you mean, phi(19, (exponent))? Or do you mean, 19? 
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