Sequences and Polynomial Congruence

In this paper we shall find a new connection between nth degree polynomial mod p congruence with n roots and higher order Fibonacci and Lucas sequences. We shall first discuss about 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

Sequences and Polynomial Congruence

In this paper we shall find a new connection between nth degree polynomial mod p congruence with n roots and higher order Fibonacci and Lucas sequences. We shall first discuss about 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

Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques

In this paper we put forward a family of algorithms for lifting solutions of a polynomial congruencemod pto polynomial congruencemod pk. For this purpose, root-finding iterative methods are employed for solving polynomial congruences of the formaxn≡b(mod pk),k≥1,wherea,b,andn>0are integers which are not divisible by an odd primep. It is shown that the algorithms suggested in this paper drastically reduce the complexity for such computations to a logarithmic scale. The efficacy of the proposed technique for solving negative exponent equations of the formax-n≡b(mod pk)has also been addressed.