Let n≥2,n∈N and let p,a1,a2,…,an,b1,b2,…,bn∈R satisfying 21≤p≤1, 0≤ai, 0≤bi≤p, i \equal{} 1, \ldots, n, and \sum^n_{i\equal{}1} a_i \equal{} \sum^n_{i\equal{}1} b_i. Prove the inequality: \sum^n_{i\equal{}1} b_i \prod^n_{j \equal{} 1, j \neq i} a_j \leq \frac{p}{(n\minus{}1)^{n\minus{}1}}. Inequalityalgebrapolynomialn-variable inequalityIMO Shortlist