Let
![(a_n)^{\infty}_{n=1}](/media/m/f/e/9/fe968e0f5842f1aa14eeed9d5101cef3.png)
be a sequence of integers with
![a_{n} < a_{n+1}, \quad \forall n \geq 1.](/media/m/e/0/3/e03bd88c869133bf00edd77d2468e786.png)
For all quadruple
![(i,j,k,l)](/media/m/d/b/2/db2ce7f8ed31bef91bb3977bfebf7540.png)
of indices such that
![1 \leq i < j \leq k < l](/media/m/e/0/0/e0052c670ee7fdc738502d1f19ad48c6.png)
and
![i + l = j + k](/media/m/7/e/7/7e7178ad9c0c3e83607693d2bf184375.png)
we have the inequality
![a_{i} + a_{l} > a_{j} + a_{k}.](/media/m/b/9/5/b958563bf9d3df2f7f3dd03c43d673c3.png)
Determine the least possible value of
![a_{2008}](/media/m/2/e/a/2ea3c08878bc4ce94cc2472c957367ce.png)
.
%V0
Let $(a_n)^{\infty}_{n=1}$ be a sequence of integers with $a_{n} < a_{n+1}, \quad \forall n \geq 1.$ For all quadruple $(i,j,k,l)$ of indices such that $1 \leq i < j \leq k < l$ and $i + l = j + k$ we have the inequality $a_{i} + a_{l} > a_{j} + a_{k}.$ Determine the least possible value of $a_{2008}$.