SE-SKOLORNAS 1976 Problem 2

For which real $a$ are there distinct reals $x$ , $y$ such that $\begin{cases} x = a - y^2 y = a - x^2 \,\, ? \end {cases}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.