IMO Shortlist 1983 problem 14
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arhiva2. travnja 2012. Is it possible to choose
![1983](/media/m/b/1/d/b1d43027c69faccfbfefd5dfccec9b02.png)
distinct positive integers, all less than or equal to
![10^5](/media/m/1/0/8/108eb30a3bde8ebb03c1e1e5eb855165.png)
, no three of which are consecutive terms of an arithmetic progression?
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Is it possible to choose $1983$ distinct positive integers, all less than or equal to $10^5$, no three of which are consecutive terms of an arithmetic progression?
Izvor: Međunarodna matematička olimpijada, shortlist 1983