Imre Z. Ruzsa
Published 2015-10-03Version 1
Let $A,B$ be sets of positive integers such that $A+B$ contains all but finitely many positive integers. S\'ark\"ozy and Szemer\'edi proved that if $ A(x)B(x)/x \to 1$, then $A(x)B(x)-x \to \infty $. Chen and Fang considerably improved S\'ark\"ozy and Szemer\'edi's bound. We further improve their estimate and show by an example that our result is nearly best possible.
Sumsets in primes containing almost all even positive integers
On the $P_1$ property of sequences of positive integers
Multiplicative subsemigroups of the positive integers closed with respect to the number of digits
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