Geodesic
On Infinite-Difference Sets
Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 897-910

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. Let A be a sequence; throughout this paper sequences are understood to be infinite, strictly increasing and composed of non-negative integers. We define D, the infinite-difference set of A, to be the set of those non-negative integers which occur infinitely often as the difference of two terms of A. Plainly D has no positive terms if and only if a i+1 — ai → ∞ as i → ∞. Note that D contains zero. We shall be interested in the case when . Then D certainly contains more than one term. In fact, see Corollary 1, §2, in this case. Here and ḏ denote the (natural asymptotic) upper and lower density respectively. 
Stewart, C. L.; Tijdeman, R. On Infinite-Difference Sets. Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 897-910. doi: 10.4153/CJM-1979-085-6
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