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
Solution: 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