The sum-product problem for integers with few prime factors

Brandon Hanson, Misha Rudnev, Ilya Shkredov +1

It was asked by E. Szemerédi if, for a finite set $A\subset \mathbb{Z}$, one can improve estimates for $\max \{|A+A|,|A\cdot A|\}$, under the constraint that all integers involved ha…