Question 19
Let $a_1,a_2,\ldots,a_{2026}$ be real numbers. Let $k$ be the largest real number such that
$$a_1^2+a_2^2+\cdots+a_{2026}^2\ge k\sum_{1\le i\lt j\le2026}a_i a_j.$$
Find the value of $\left\lfloor\left|\frac1k\right|\right\rfloor$.
$$a_1^2+a_2^2+\cdots+a_{2026}^2\ge k\sum_{1\le i\lt j\le2026}a_i a_j.$$
Find the value of $\left\lfloor\left|\frac1k\right|\right\rfloor$.