Find the remainder ofProblem:

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 . ThusSolution:

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