Question 90
Find all natural numbers $a$, $b$ and $c$ that satisfy the equation
$$
\frac{a+b}{a+c}=\frac{b+c}{b+a}
$$
and for which $ab+ac+bc$ is considered to be a prime number.
$$
\frac{a+b}{a+c}=\frac{b+c}{b+a}
$$
and for which $ab+ac+bc$ is considered to be a prime number.