# Modular arithmetic

• May 3rd 2011, 04:39 PM
nicola5
Modular arithmetic
So how does one calculate say 2^9 in the filed F_11( the set of integers of mod11 wrt multiplication)?
Simple , I know but I just cant seem to get it!!!
• May 3rd 2011, 07:28 PM
tonio
Quote:

Originally Posted by nicola5
So how does one calculate say 2^9 in the filed F_11( the set of integers of mod11 wrt multiplication)?
Simle , I know but I just cant seem to get it!!!

Well, it's easy to check that 2^5 = -1 (mod 11) , so...

Tonio
• May 4th 2011, 12:07 AM
chisigma
Quote:

Originally Posted by nicola5
So how does one calculate say 2^9 in the filed F_11( the set of integers of mod11 wrt multiplication)?
Simle , I know but I just cant seem to get it!!!

The 11 is a prime number so that http://quicklatex.com/cache3/ql_fce9...05ef7d9_l3.png is http://quicklatex.com/cache3/ql_2e5c...a9effab_l3.png and that means that...

http://quicklatex.com/cache3/ql_d837...66a2b26_l3.png (1)

... which is the multiplicative inverse of 2 You will easily find... in is 'interesting' the fact that the same result You arrive also for [among many other examples...] http://quicklatex.com/cache3/ql_3bc6...3ecdbbb_l3.png (Wink)...

Kind regards

$\chi$ $\sigma$