Question 15
Let us consider three natural numbers $a, b, c$ such that the ratio $$
\frac{a+b+c}{a b c}
$$ is the inverse of an integer and positive $k$ number. It is requested to demonstrate:
a) $a^{3}+b^{3}+c^{3}$ is not prime.
b) For each $k \in \mathbb{N}$ there are triples of natural $a, b, c$ that meet the conditions.
\frac{a+b+c}{a b c}
$$ is the inverse of an integer and positive $k$ number. It is requested to demonstrate:
a) $a^{3}+b^{3}+c^{3}$ is not prime.
b) For each $k \in \mathbb{N}$ there are triples of natural $a, b, c$ that meet the conditions.