Question 21
Find all the triples $(a, b, c)$ of integer numbers, fulfilling the relations
$$
a^2 + a = b + c, \quad b^2 + b = a + c, \quad c^2 + c = a + b.
$$
$$
a^2 + a = b + c, \quad b^2 + b = a + c, \quad c^2 + c = a + b.
$$
MathNet 2023-part-05 — 191 problems (EN–VI) Question 21
Math Olympiad Vault · MathNet 2023-part-05 — 191 problems (EN–VI)