On the system of double equations with three unknowns $d+ay+bx+cx^2=z^2 , y+z=x^2$

Abstract

‎The system of double equations with three unknowns given by $d+ay+bx+cx^2=z^2‎ , ‎y+z=x^2$ 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.