Chains of quadratic residues

Abstract:

The problem considered in this paper is that of finding longest chains of the type: ${r_1},{r_2},{r_3}, \cdots ,{r_m}$, for which the $m(m + 1)/2$ sums ${r_i} + {r_{i + 1}} + {r_{i + 2}} + \cdots + {r_j},1 \leqq i \leqq j \leqq m$, will be distinct quadratic residues of a given prime p.