Problems and results on additive properties of general sequences. V
[Part I, cf. Pac. J. Math. 118, 347--357 (1985; Zbl 0569.10032), part IV, cf. Lect. Notes Math. 1122, 85--104 (1985; Zbl 0588.10056).] A very special case of one of the theorems of the authors states as follows: Let \(1\leq a_1\leq a_2\leq\dots\) be an infinite sequence of integers for which all the sums \(a_i+a_j\), \(1\leq i\leq j\), are distinct. Then there are infinitely many integers \(k\) for which \(2k\) can be represented in the form \(a_i+a_j\) but \(2k+1\) cannot be represented in this form. Several unsolved problems are stated.
scientific article; zbMATH DE number 3961754