When , find the remainder when

.

Have no idea how to approach this problem, any help would be appreciated ;)

I've got the hint that , thinking that the solutions involves and ?

Thanks in advance for the help

Craig

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- Dec 3rd 2009, 02:16 PMcraigPossible Congruence Question
When , find the remainder when

.

Have no idea how to approach this problem, any help would be appreciated ;)

I've got the hint that , thinking that the solutions involves and ?

Thanks in advance for the help

Craig - Dec 3rd 2009, 02:47 PMDrexel28
Find the remainder of**Problem:**

Note that this is equivalent to asking what is the smallest positive remainder of the above. So realize though that . To do this we work in mods, namely we compute . Note though that . Also, note that . And since and we see then by Euler's theorem that . Lastly we see that . Thus our final answer is , but since we wanted the positive remainder we add to the numerator to arrive at . Thus__Solution:__

- Wolfram|Alpha - Dec 3rd 2009, 03:31 PMcraig
Hi thanks a lot for your reply. I was following you until this bit:

I know that .

But I'm not sure how you got to this result,

Quote:

we see then by Euler's theorem that

Thanks again for the help

Craig - Dec 3rd 2009, 04:32 PMDrexel28