The prime year 2017

What is the remainder of 201 8 2017 + 2016 2018^{2017}+2016 divided by 2017?


The answer is 0.

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1 solution

201 8 2017 + 2016 ( 2017 + 1 ) 2017 + 2016 1 2017 + 2016 1 + 2016 2017 0 (mod 2017) \begin{aligned} 2018^{2017} + 2016 & \equiv (2017+1)^{2017} + 2016 \equiv 1^{2017} + 2016 \equiv 1+2016 \equiv 2017 \equiv \boxed 0 \text{ (mod 2017)} \end{aligned}

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