Difference between revisions of "2013 IMO Problems/Problem 5"
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Let <math>\mathbb Q_{>0}</math> be the set of all positive rational numbers. Let <math>f:\mathbb Q_{>0}\to\mathbb R</math> be a function satisfying the following three conditions: | Let <math>\mathbb Q_{>0}</math> be the set of all positive rational numbers. Let <math>f:\mathbb Q_{>0}\to\mathbb R</math> be a function satisfying the following three conditions: | ||
Revision as of 12:49, 21 June 2018
Problem
Let be the set of all positive rational numbers. Let
be a function satisfying the following three conditions:
(i) for all , we have
;
(ii) for all
, we have
;
(iii) there exists a rational number
such that
.
Prove that for all
.
Proposed by Bulgaria