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Functional equation f(x+y)=f(x)+f(y) on a restricted domain

Source: XIX Olimpíada Matemática Rioplatense (2010)

July 22, 2011
algebrafunctiondomainalgebra unsolved

Problem Statement

Find all the functions f:N→Rf:\mathbb{N}\to\mathbb{R} that satisfy f(x+y)=f(x)+f(y) f(x+y)=f(x)+f(y) for all x,y∈Nx,y\in\mathbb{N} satisfying 106−1106<xy<106+110610^6-\frac{1}{10^6} < \frac{x}{y} < 10^6+\frac{1}{10^6}.
Note: N\mathbb{N} denotes the set of positive integers and R\mathbb{R} denotes the set of real numbers.
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