The equation $(j+k+1)^2-4k = Qn^2$ and related dispersions
J. Integer Seq. 10(2), Article 07.2.7, 17 p., electronic only (2007)
Summary
Summary: Suppose $Q$ is a positive nonsquare integer congruent to 0 or 1 mod 4. Then for every positive integer $n$, there exists a unique pair $(j,k) of positive integers such that (j+k+1)$^2-4k = Qn^2$ . This representation is used to generate the fixed-$j$ array for $Q$ and the fixed-$k$ array for $Q$. These arrays are proved to be dispersions; i.e., each array contains every positive integer exactly once and has certain compositional and row-interspersion properties.$
