### IMO Shortlist 2017 problem N2

Kvaliteta:

Avg: 0,0Težina:

Avg: 6,0Let be a prime number. Eduardo and Fernando play the following game making moves alternately: in each move, the current player chooses an index in the set that was not chosen before by either of the two players and then chooses an element from the set . Eduardo has the first move. The game ends after all the indices have been chosen .Then the following number is computed: . The goal of Eduardo is to make divisible by , and the goal of Fernando is to prevent this.

Prove that Eduardo has a winning strategy.

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