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Sequence

Source: Junior Olympiad of Malaysia Shortlist 2015 A4

July 17, 2015
algebranumber theory

Problem Statement

Suppose 2015=a1<a2<a3<⋯<ak 2015= a_1 <a_2 < a_3<\cdots <a_k be a finite sequence of positive integers, and for all m,n∈N m, n \in \mathbb{N} and 1≤m,n≤k1\le m,n \le k , am+an≥am+n+∣m−n∣ a_m+a_n\ge a_{m+n}+|m-n| Determine the largest possible value k k can obtain.
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