Year: 2025
Type: article
Abstract: We study the modular resolution method using a new tool called a Polyserie introduced by Wildberger N.J. & Rubine D. to prove an equivalence theorem of the existence and the unicity of the solution of the equation of the form Ht2(x) – Ht(x)+t ≡ 0 (mod tn). These equations admits solutions for a fixed t but when t changes in a range of several values, then the equation becomes parametric and hence the solution should be parametric too. Prof. Wildberger N.J has studied such equations using Catalan numbers sequence using the recurrence formula between their terms Cn+1 = ∑k=0n Ck Cn-k, which allow us to easily prove the main result of the present article. We study Wildberger’s Polynumber Sequences, Binomial Chu-Vandermonde Identity, Truncated Polyseries and finally Modular Resolution as Application.
Author: Mahdi-Tahar Brahimi
Institution: University Mohamed Boudiaf of M'sila
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416897401