MathDB
F(F(n^163)) = F(F(n)) + F(F(361))

Source: IMO Shortlist 1995, S1

August 10, 2008
algebraIMO Shortlistfunctional equationIteration

Problem Statement

Does there exist a sequence F(1),F(2),F(3),… 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,… 0, 1, 2, \ldots occurs in the sequence. (b) Each positive integer occurs in the sequence infinitely often. (c) For any n≥2, n \geq 2, F(F(n^{163})) \equal{} F(F(n)) \plus{} F(F(361)).
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