2000 OIM Problems/Problem 4

Problem

From an infinite arithmetic progression $1, a_l, a_2, \cdots$ of real numbers, terms are eliminated, obtaining an infinite geometric progression $1, a_{n1}, a_{n2}, \cdots$ of ratio $q$. Find all possible values of q.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe15.htm