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\sum_{k=1}^{N} k^{2018} is divisible by 2018?

Source: 2019 Dürer Math Competition Finals Day2 E+11 https://artofproblemsolving.com/community/c1621835_2019_

January 5, 2022
Sumdividesdivisiblenumber theory

Problem Statement

What is the smallest NN for which ∑k=1Nk2018\sum_{k=1}^{N} k^{2018} is divisible by 20182018?
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