Question 177
Find, with reasons, all integers $a$, $b$, and $c$ such that
$$
\frac{1}{2}(a+b)(b+c)(c+a) + (a+b+c)^3 = 1 - abc.
$$
$$
\frac{1}{2}(a+b)(b+c)(c+a) + (a+b+c)^3 = 1 - abc.
$$
MathNet 2003 — Part 01 Question 177
Math Olympiad Vault · MathNet 2003 — Part 01