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Distinct positive integers that do not contain a 9

Source: IMO Longlist 1989, Problem 19

September 18, 2008
inequalitiesnumber theory unsolvednumber theory

Problem Statement

Let a1,…,an a_1, \ldots, a_n be distinct positive integers that do not contain a 9 9 in their decimal representations. Prove that the following inequality holds \sum^n_{i\equal{}1} \frac{1}{a_i} \leq 30.
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