Binomial Symbols and Prime Moduli

TL;DR

This paper investigates properties of binomial symbols modulo prime numbers, building on prior work to improve results related to periodic sequences inspired by Olympiad problems.

Contribution

It advances previous findings by providing improved results on the periodicity of sequences derived from binomial symbols modulo primes.

Findings

Established a new, shorter period for the sequence

Extended the class of primes for which the sequence's properties hold

Improved bounds on the sequence's behavior

Abstract

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).