IMO Shortlist 1993 problem A6


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 8,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
Let \mathbb{N} = \{1,2,3, \ldots\}. Determine if there exists a strictly increasing function f: \mathbb{N} \mapsto \mathbb{N} with the following properties:

(i) f(1) = 2;

(ii) f(f(n)) = f(n) + n, (n \in \mathbb{N}).
Izvor: Međunarodna matematička olimpijada, shortlist 1993