Question 131
Let $\left(a_{n}\right)_{n=1}^{\infty}$ be a sequence of positive integers such that $a_{n} \lt a_{n+1}$ for all $n \geqslant 1$. Suppose that for all quadruples of indices $(i, j, k, l)$ such that $1 \leqslant i \lt j \leqslant k \lt l$ and $i+l=j+k$, the inequality $a_{i}+a_{l} \gt a_{j}+a_{k}$ is satisfied. Determine the least possible value of $a_{2008}$.