On the Existence of Perfect Splitter Sets · arXivDesk1903.00118Mar 1, 2019
On the Existence of Perfect Splitter Sets
Pingzhi Yuan, Kevin Zhao
Abstract
Given integers k1,k2 with 0≤k1<k2
, the determinations of all positive integers
for which there exists a perfect Splitter
B[−k1,k2](q) set is a wide open question in general. In this paper, we obtain new necessary and sufficient conditions for an odd prime
such that there exists a nonsingular perfect
B[−1,3](p) set. We also give some necessary conditions for the existence of purely singular perfect splitter sets. In particular, we determine all perfect
B[−k1,k2](2n) sets for any positive integers
with
k1+k2≥4 . We also prove that there are infinitely many prime
such that there exists a perfect
B[−1,3](p) set.