IMO Shortlist 1995 problem S1
Dodao/la:
arhiva2. travnja 2012. Does there exist a sequence
![F(1), F(2), F(3), \ldots](/media/m/5/a/c/5acaa41fdd6fc3841accfa6762bf2333.png)
of non-negative integers that simultaneously satisfies the following three conditions?
(a) Each of the integers
![0, 1, 2, \ldots](/media/m/9/4/0/940e5efeb8870a45e3db6768e55f8d63.png)
occurs in the sequence.
(b) Each positive integer occurs in the sequence infinitely often.
(c) For any
%V0
Does there exist a sequence $F(1), F(2), F(3), \ldots$ of non-negative integers that simultaneously satisfies the following three conditions?
(a) Each of the integers $0, 1, 2, \ldots$ occurs in the sequence.
(b) Each positive integer occurs in the sequence infinitely often.
(c) For any $n \geq 2,$
$$F(F(n^{163})) = F(F(n)) + F(F(361)).$$
Izvor: Međunarodna matematička olimpijada, shortlist 1995