Nemotron-IMO-Bench 2026 C50

Prove that there are $c,n_0>0$ such that for any set $A$ consisting of $n>n_0$ integers we have $$|A-A|-|A+A|\leq n^2-cn^{8/5},$$ where $A\pm A=\{a\pm b| a,b\in A\}$.