Binomial Symbols and Prime Moduli

We try to improve a problem asked in an Indian Math Olympiad. We give a brief overview of the work done in Saikia and Vogrinc (2011) and Saikia and Vogrinc where the authors have found a periodic sequence and the length of its period, all inspired from an Olympiad problem. The main goal of the paper is to improve the main result in Saikia and Vogrinc (2011).