On the system of double equations with three unknowns d + ay + bx + cx2 = z2, y + z = x2

Abstract

The system of double equations with three unknowns given by d + ay + bx + cx2 = z2, y + z = x2 is analysed for its infinitely many non-zero distinct integer solutions. Different sets of integer solutions have been presented. A few interesting relations among the solutions are given. © 2021, Semnan University, Center of Excellence in Nonlinear Analysis and Applications. All rights reserved.