IMO 2008 Shortlist A6

Let f : R → N be a function which satisfies f  x + f(y)  = f  y + f(x)  for all x,y ∈ R. (1) Prove that there is a p...

imomathematicsolympiadshortlistalgebra

IMO 2008 Shortlist A6

Category: Algebra

Problem

Let f : R → N be a function which satisfies f  x + f(y)  = f  y + f(x)  for all x,y ∈ R. (1) Prove that there is a positive integer which is not a value of f.