The relationship between algebraic equations and $(n,m)$-forms, their degrees and recurrent fractions - I.I. Lishchynsky (Karpatsʹkì Matematičnì Publìkacìï, 2019)
Algebraic and recursion equations are widely used in different areas of mathematics, so various objects and methods of research that are associated with them are very important. In this article we investigate the relationship between $(n,m)$-forms with generalized Diophantine Pell's equation, algebraic equations of $n$ degree and recurrent fractions. The properties of the $(n,m^n+1)$-forms and their characteristic equation are considered. The author applied parafunctions of triangular matrices to the study of algebraic equations and corresponding recurrence equations. The form of adjacent roots of the annihilating polynomial of arbitrary $(n,m)$-forms over the field of rational numbers are explored.