MathDB
Positive integer inequality

Source: 43rd International Tournament of Towns, Junior A-Level P6, Fall 2021

February 18, 2023
inequalitiesalgebraTournament of Towns

Problem Statement

Prove that for any positive integers a1,a2,…,ana_1, a_2, \ldots , a_n the following inequality holds true: ⌊a12a2⌋+⌊a22a3⌋+⋯+⌊an2a1⌋⩾a1+a2+⋯+an.\left\lfloor\frac{a_1^2}{a_2}\right\rfloor+\left\lfloor\frac{a_2^2}{a_3}\right\rfloor+\cdots+\left\lfloor\frac{a_n^2}{a_1}\right\rfloor\geqslant a_1+a_2+\cdots+a_n. Maxim Didin
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