Question 142
Prove that there do not exist pairwise distinct complex numbers $a$, $b$, $c$, and $d$ such that
$$
a^{3}-b c d=b^{3}-c d a=c^{3}-d a b=d^{3}-a b c .
$$
$$
a^{3}-b c d=b^{3}-c d a=c^{3}-d a b=d^{3}-a b c .
$$
MathNet 2023-part-07 — 187 problems (EN–VI) Question 142
Math Olympiad Vault · MathNet 2023-part-07 — 187 problems (EN–VI)