MathDB
Czech-Slovak-Polish match 2001

Source: Titu Andreescu 2000-2001 , page 253

February 22, 2004
inequalitiesn-variable inequalityHolderConvexity

Problem Statement

Let n≥2n\ge2 be a natural number, and aia_i be positive numbers, where i=1,2,⋯ ,n.i=1,2,\cdots,n. Show that (a13+1)(a23+1)⋯(an3+1)≥(a12a2+1)(a22a3+1)⋯(an2a1+1)\left(a_1^3+1\right)\left(a_2^3+1\right)\cdots\left(a_n^3+1\right) \geq \left(a_1^2a_2+1\right)\left(a_2^2a_3+1\right)\cdots\left(a_n^2a_1+1\right)
Back to ProblemsView on AoPS