IMO Shortlist 2017 problem N3


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Dodao/la: arhiva
3. listopada 2019.
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Determine all integers n\geq 2 having the following property: for any integers a_1,a_2,\ldots, a_n whose sum is not divisible by n, there exists an index 1 \leq i \leq n such that none of the numbers a_i,a_i+a_{i+1},\ldots,a_i+a_{i+1}+\ldots+a_{i+n-1}is divisible by n. Here, we let a_i=a_{i-n} when i >n.

Izvor: https://www.imo-official.org/problems/IMO2017SL.pdf