IMO Shortlist 2017 problem N2
Let 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.