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Increasing functions

Source: Romanian MO 2004, 9th grade, Problem 1

February 26, 2006
functioninequalitiesalgebra proposedalgebra

Problem Statement

Find the strictly increasing functions f:{1,2,…,10}→{1,2,…,100}f : \{1,2,\ldots,10\} \to \{ 1,2,\ldots,100 \} such that x+yx+y divides xf(x)+yf(y)x f(x) + y f(y) for all x,y∈{1,2,…,10}x,y \in \{ 1,2,\ldots,10 \}. Cristinel Mortici
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