Modular arithmetic

**nicola5** · May 3rd 2011, 04:39 PM

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!!!

**tonio** · May 3rd 2011, 07:28 PM

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

**chisigma** · May 4th 2011, 12:07 AM

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

is

and that means that...

(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...]

...

Kind regards

$\chi$ $\sigma$

Math Help - Modular arithmetic

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