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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].

##### MSC:
 11B83 Special sequences and polynomials 11D04 Linear Diophantine equations
##### Keywords:
density; stable sets; upper asymptotic density; linear equation