Question 52
Let n≥5 be an integer and let $a_1,\ldots,a_n$ be pairwise distinct integers in {1,…,2n}. Prove that there are distinct indices i,j in {1,…,n} such that
$$\operatorname{lcm}(a_i,a_j)\le6\left(E\left(\frac n2\right)+1\right),$$
where E(x) denotes the integer part of x.
$$\operatorname{lcm}(a_i,a_j)\le6\left(E\left(\frac n2\right)+1\right),$$
where E(x) denotes the integer part of x.