Abstract
We investigate the r( A ; n) number of solutions of n = a + a0, a0, where aand a0 belong to a given in finite A ˆ N . We disprove a conjecture of Erd}os and Freud by constructing an A which satisfies r( A ; n) 3 for all n, but r( A ; n) = 1 holds only for finitely many values of n. Several related problems are discussed, as well.
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Sándor, C. Range of bounded additive representation functions. Periodica Mathematica Hungarica 42, 169–177 (2001). https://doi.org/10.1023/A:1015261010544
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DOI: https://doi.org/10.1023/A:1015261010544