Question 164
Find all triples of positive integers $a$, $b$ and $c$, for which the expression
$$
T = \frac{(a + 1)(b + 1)(c + 1) - 12}{abc}
$$
is an integer.
$$
T = \frac{(a + 1)(b + 1)(c + 1) - 12}{abc}
$$
is an integer.
MathNet 2023-part-03 — 191 problems (EN–VI) Question 164
Math Olympiad Vault · MathNet 2023-part-03 — 191 problems (EN–VI)