Finding integral diagonal pairs in a two dimensional N-set

Lev A. Borisov, Renling Jin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2431-2434
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number7
StatePublished - Jul 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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