Sequences and Polynomial Congruence

TL;DR

This paper explores new relationships between polynomial congruences of degree n with n roots and higher-order Fibonacci and Lucas sequences, advancing understanding of their interconnected properties.

Contribution

It introduces novel connections between polynomial congruences and higher-order Fibonacci and Lucas sequences, expanding the theoretical framework of sequence-polynomial relationships.

Findings

Established new links between polynomial congruences and higher-order sequences

Derived relations between recurrence relations and sequence congruences

Enhanced understanding of sequence behavior modulo primes

Abstract

In this paper, we shall find a new connection between $n$th degree polynomial mod $p$ congruence with $n$ roots and higher-order Fibonacci and Lucas sequences. We shall first discuss the recent work been done in sequences and their connection to polynomial congruence and then find out new relations between particular recurrence relation and the congruence of the sequences.