# elementary number theory – What is the remainder when \$1^{2016} + 2^{2016}+ 3^{2016}+…+2016^{2016} \$ is divided by \$2017\$

What is the remainder when $$1^{2016} + 2^{2016}+ 3^{2016}+…+2016^{2016}$$ is divided by $$2017$$

I saw a quesiton in stack-exchange : What is the remainder when \$1^{2016} + 2^{2016} + ⋯ + 2016^{2016}\$ is divided by \$2016\$?

When i checking over it , i thought that what if it is divided $$2017$$ instead of $$2016$$. The answer was easy to me in the first glance because by using phi function ,the summation must have been equal to $$2016$$ and $$2016 mod(2017)=2016$$.

However the answer is equal to $$1759$$ according to python. What am i missing ?