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Functional inequality condition

Source: Italy TST 1995

November 22, 2010
inequalitiesfunctionalgebrafunctional equationalgebra solvedBoundingItaly TST

Problem Statement

A function f:Rā†’Rf:\mathbb{R}\rightarrow\mathbb{R} satisfies the conditions \begin{cases}f(x+24)\le f(x)+24\\ f(x+77)\ge f(x)+77\end{cases} \text{for all}\ x\in\mathbb{R} Prove that f(x+1)=f(x)+1f(x+1)=f(x)+1 for all real xx.
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