Prove that the inequality \[ \prod_{i=1}^n\prod_{j=1}^n\left(1+|a_i+a_j|\right)\geq \prod_{i=1}^n\prod_{j=1}^n\left(1+|a_i-a_j|\right)\] holds for any real numbers $a_1,\ldots,a_n$. We have not received any solutions. For a detailed solution and some related problems see the following link {{:pow:2022fproblem6.pdf|Solution}}.