Let be a real-valued polynomial function of the form , where the degree of in is greater than or equal to . 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. In this paper, we prove that (i) the leading coefficient must be a factor of , and (ii) each solution of () is of the form , where is arbitrary and is also a factor of , for some constant , provided the equation has infinitely many quasi-coincidence (point) solutions.
"New Quasi-Coincidence Point Polynomial Problems." J. Appl. Math. 2013 (SI21) 1 - 8, 2013. https://doi.org/10.1155/2013/959464