OMM 1988 Problem 7

Si $A$ y $B$ son subconjuntos ajenos del conjunto $\{1, 2, \ldots, m-1, m\}$ y la suma de los elementos de $A$ es igual a la suma de los elementos de $B$ , pruebe que el número de elementos de $A$ y también de $B$ es menor que $\frac{m}{\sqrt{2}}$ .

Official text Mexican Mathematical Olympiad 1988 official paper, page 1. Quoted with source.

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