Physical Sciences and Mathematics Commons^™

On Translations Of Quadratic Residues, Bruce Brandt

Journal of the Minnesota Academy of Science

The question is posed: Given a set, S, and a positive integer, k, does a function from k to S exist such that, letting x - y if x is a member of a k-tuple going toy, we never have x - y and y - x? The question is linked to whether circular translations of quadratic residues intersect. Several conjectures are made related to the heuristic that quadratic residues are more inclined to intersect their circular translation than other subsets of Z/nZ with the same number of elements.