Question 11
Find the least positive integer $n$ (if it exists) such that $\displaystyle\sum_{k=1}^n a_k\cdot k^2=2026$, where each $a_k$ is either $1$ or $-1$ for all $k=1,2,3,\ldots,n$.
(Note: If you think that such an $n$ does not exist, enter your answer as 0.)
(Note: If you think that such an $n$ does not exist, enter your answer as 0.)