Let be a real-valued polynomial function of the form where the degree of in is greater than . For arbitrary polynomial function , , we will find a polynomial solution to satisfy the following equation (): where is a constant depending on the solution , namely a quasi-coincidence (point) solution of (), and is called a quasi-coincidence value of (). In this paper, we prove that the number of all solutions in () does not exceed provided those solutions are of finitely many exist, if all solutions are of infinitely many exist, then any solution is represented as the form where is arbitrary and is also a factor of , provided the equation () has infinitely many quasi-coincidence (point) solutions.
"Infinitely Many Quasi-Coincidence Point Solutions of Multivariate Polynomial Problems." Abstr. Appl. Anal. 2013 (SI09) 1 - 9, 2013. https://doi.org/10.1155/2013/307913