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On an additive property of stable sets. (English) Zbl 0924.11011
Greaves, G. R. H. (ed.) et al., Sieve methods, exponential sums, and their applications in number theory. Proceedings of a symposium, Cardiff, UK, July 17–21, 1995. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 237, 55-63 (1997).
The authors prove the following theorem: Let \(a,b >0\) and \(c\neq 0\) be integers with \((a,b)\mid c\). If \(\mathcal {A}\) is a stable set with non-zero upper asymptotic density, then the linear equation \(am-bn+c=0\) has infinitely many solutions with \(m,n \in {\mathcal A}\).
For the entire collection see [Zbl 0910.00038].

11B83 Special sequences and polynomials
11D04 Linear Diophantine equations