IMO 2023 Shortlist C2

Determine the maximal length L of a sequence a1,...,aL of positive integers satisfying both the following properties: • ...

IMO 2023 Shortlist C2

Category: Combinatorics

Problem

Determine the maximal length L of a sequence a1,...,aL of positive integers satisfying both the following properties: • every term in the sequence is less than or equal to 22023 , and • there does not exist a consecutive subsequence ai,ai1,...,aj (where 1 ď i ď j ď L) with a choice of signs si,si1,...,sj P t1,´1u for which siai si1ai1 ¨¨¨ ` sjaj “ 0. (Czech Republic)