Problem 1194

Let $A\subset\mathbb{N}$ be such that every integer $n\geq 1$ can be written uniquely as $a_n-b_n$ for some $a_n,b_n\in A$ . How fast must $a_n/n$ increase?

Source: erdosproblems.com/1194

Additive combinatorics
Additive bases
Sidon sets

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CiNa08: Cilleruelo, Javier and Nathanson, Melvyn B., Perfect difference sets constructed from Sidon sets. Combinatorica (2008), 401-414.
Er80: Erdős, Paul, A survey of problems in combinatorial number theory. Ann. Discrete Math. (1980), 89-115.
HaRo66: Halberstam, H. and Roth, K. F., Sequences. Vol. I. (1966), xx+291.
Le04: Lev, Vsevolod F., Reconstructing integer sets from their representation functions. Electron. J. Combin. 11 (2004), Research Paper 78, 6 pp.

Problem 1194

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