Modular resolutions by polyseries

We study the modular resolution method using new tools called polynumbers and polyseries, introduced by Prof. Wildberger N.J. We try to prove an equivalence theorem of the existence and the uniqueness of the solutions of the modular quadratic equations, using the recurrence formula between the Catalan sequence terms and introducing the following notions: Wildberger’s polynumber sequences (polynomials), binomial Chu-Vandermonde identity and truncated polyseries.