Let (an)∞n=1 be a sequence of integers with an<an+1,∀n≥1. For all quadruple (i,j,k,l) of indices such that 1≤i<j≤k<l and i+l=j+k we have the inequality ai+al>aj+ak. Determine the least possible value of a2008.
Source: MEMO 2008, Single, Problem 1
Tags: inequalities, algebra unsolved, algebra
Let (an)∞n=1 be a sequence of integers with an<an+1,∀n≥1. For all quadruple (i,j,k,l) of indices such that 1≤i<j≤k<l and i+l=j+k we have the inequality ai+al>aj+ak. Determine the least possible value of a2008.