According to Nathanson, an n-dimensional N-set is a compact subset A of ℝn such that for every x ε ℝn there is y ε A with y - x ε ℤn. We prove that every two dimensional N-set A must contain distinct points x, y such that x - y is in ℤ2 and x - y is neither horizontal nor vertical. This answers a question of P. Hegarty and M. Nathanson.
All Science Journal Classification (ASJC) codes
- Applied Mathematics