I am really having trouble understanding how to do these questions, and I have read up on google, but still struggling

I need to be able to do this question without a calculator, and i am not sure how to do it? Any help appreciated.

Printable View

- November 17th 2013, 09:21 AMTweetymodulo arithmetic help
I am really having trouble understanding how to do these questions, and I have read up on google, but still struggling

I need to be able to do this question without a calculator, and i am not sure how to do it? Any help appreciated. - November 17th 2013, 04:22 PMchiroRe: modulo arithmetic help
Hey Tweety.

The easiest way to do this is to use powers of 2. Look at 5 mod 11, then 5^2, then 5^4, 5^8, then 5^10 and finally 5^11.

As an example 5 mod 9 = 5. 5^2 mod 9 = 25 mod 9 = -2. 5^4 = (-2)^2 mod 9 = 4. 5^8 mod 9 = 16 mod 9 = -2. 5^11 mod 9 = -2*-2*5 mod 9 = 20 mod 9 = 2.

Check to see if I have made a mistake, but the process used above is the basic idea in solving these kinds of problems. - November 18th 2013, 06:49 AMHartlwRe: modulo arithmetic help
Using modular arithmetic of remainder classes: [a][b]=[ab]:

[5][5]=[25]=[7]

[5]^{3}=[35]=[8]

[5]^{4}=[40]=[4]

[5]^{5}=[20]=[2]

[5]^{11}=[2][2][5]=[20]=[2] - November 18th 2013, 11:20 AMTweetyRe: modulo arithmetic help