The solvability of the equation a1a2. ak = x2, a1, a2., ak ε(lunate) A is studied for fixed k and 'dense' sets A of positive integers. In particular, it is shown that if k is even and k ≥ 4, and A is of positive upper density, then this equation can be solved.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics