Problem

Source: IMO ShortList 2008, Algebra problem 6

Tags: function, algebra, functional equation, range, IMO Shortlist



Let f:RN be a function which satisfies f(x+1f(y))=f(y+1f(x)) for all x, yR. Prove that there is a positive integer which is not a value of f. Proposed by Žymantas Darbėnas (Zymantas Darbenas), Lithuania