Let $p > 3$ be prime. Is is true that there exists $x \in \mathbb{Z}_p$ such that $$ (1+x^2)^3-1 $$ is not a square in $\mathbb{Z}_p$? Equivalently, can we show that the equation $$ -y^2 = (1+x^2)^3-1 $$ always has non-trivial solutions $(x,y) \ne (0,0)$ in $\mathbb{Z}_p$?