MathDB

Determine the least possible value of a_(2008)

Source: MEMO 2008, Single, Problem 1

September 10, 2008

inequalitiesalgebra unsolvedalgebra

Problem Statement

Let (a_n)^{\infty}_{n\equal{}1} be a sequence of integers with a_{n} < a_{n\plus{}1}, \forall n \geq 1. For all quadruple

(i,j,k,l)

of indices such that

1 \leq i < j \leq k < l

and i \plus{} l \equal{} j \plus{} k we have the inequality a_{i} \plus{} a_{l} > a_{j} \plus{} a_{k}. Determine the least possible value of

a_{2008}.