IMO 2018 Shortlist N7
Let n ě 2018 be an integer, and let a1,a2,...,an,b1,b2,...,bn be pairwise distin t positive integers not ex eeding 5n. S...
Category: Number Theory
Problem
Let n ě 2018 be an integer, and let a1,a2,...,an,b1,b2,...,bn be pairwise distin t positive integers not ex eeding 5n. Suppose that the sequen e a1 b1 , a2 b2 , ..., an bn forms an arithmeti progression. Prove that the terms of the sequen e are equal. (Thailand) 8 Cluj-Napo a Romania, 314 July 2018 Shortlisted problems solutions 9