Problem

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Tags: inequalities, induction, number theory proposed, number theory



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