IMO Shortlist 1993 problem A6
Dodao/la:
arhiva2. travnja 2012. Let
![\mathbb{N} = \{1,2,3, \ldots\}](/media/m/1/2/3/1230b3e863395e4d12c056415c28f4d0.png)
. Determine if there exists a strictly increasing function
![f: \mathbb{N} \mapsto \mathbb{N}](/media/m/0/6/4/064f5e79a7f8bd81b5e7163e70e87d6b.png)
with the following properties:
(i)
![f(1) = 2](/media/m/2/c/a/2ca4dff86a2660492947451bd133c684.png)
;
(ii)
![f(f(n)) = f(n) + n, (n \in \mathbb{N})](/media/m/d/2/b/d2bbfbb8a5d93681ca45d19a06716951.png)
.
%V0
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