MathDB

Prove the inequality - Iran NMO 2009 - Problem 5

Source:

September 20, 2010

inequalitiesinductionnumber theory proposednumber theory

Problem Statement

Let

a_1<a_2<\cdots<a_n

be positive integers such that for every distinct

1\leq{i,j}\leq{n}

we have

a_j-a_i

divides

a_i

. Prove that

ia_j\leq{ja_i} \qquad \text{ for } 1\leq{i}<j\leq{n}