Difference between revisions of "1993 IMO Problems/Problem 5"
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==Problem== | ==Problem== | ||
| + | Let <math>\mathbb{N} = \{1,2,3, \ldots\}</math>. Determine if there exists a strictly increasing function <math>f: \mathbb{N} \mapsto \mathbb{N}</math> with the following properties: | ||
| + | |||
| + | (i) <math>f(1) = 2</math>; | ||
| + | |||
| + | (ii) <math>f(f(n)) = f(n) + n, (n \in \mathbb{N})</math>. | ||
==Solution== | ==Solution== | ||
Revision as of 02:10, 5 July 2020
Problem
Let 
. Determine if there exists a strictly increasing function 
with the following properties:
(i) 
;
(ii) 
.
