On a sumset problem for integers
Summary: Let \(A\) be a finite set of integers. We show that if \(k\) is a prime power or a product of two distinct primes then \[ |A+k\cdot A|\geq(k+1)|A|-\lceil k(k+2)/4\rceil \] provided \(|A|\geq (k-1)^{2}k!\), where \(A+k\cdot A=\{a+kb:\;a,b\in A\}\). We also establish the inequality \(|A+4\cdot A|\geq5|A|-6 \) for \(|A|\geq5\).
scientific article; zbMATH DE number 6340111
scientific article