Intersections of Sumsets in Additive Number Theory

Key Points

• The aim is to determine when the h-fold sumset of an intersection of sets equals the intersection of their h-fold sumsets.
• Defined a sequence of sets in an additive abelian semigroup
• Analyzed conditions for equality using mathematical set theory
• Delineated specific conditions under which $$ hA = \bigcap_{q=1}^{\infty} hA_q $$ holds for $h \geq 2$
• Identified characteristics of the sequence $(A_q)$ needed for the equality to occur