MathNet 2009-part-05 — 172 problems (EN–VI) Question 89

Let $f(x) = 2x^{3} - 2x$. For what positive values of $a$ do there exist distinct $b, c, d$ such that $(a, f(a))$, $(b, f(b))$, $(c, f(c))$, $(d, f(d))$ is a rectangle?