19

Part of 1989 IMO Longlists

Problems(1)

Distinct positive integers that do not contain a 9

Source: IMO Longlist 1989, Problem 19

a_1, \ldots, a_n

be distinct positive integers that do not contain a

9

in their decimal representations. Prove that the following inequality holds \sum^n_{i\equal{}1} \frac{1}{a_i} \leq 30.

inequalitiesnumber theory unsolvednumber theory