Question 96
Find all the triples of non-negative integers $(a, b, c)$ for which the number
$$
\frac{(a+b)^4}{c} + \frac{(b+c)^4}{a} + \frac{(c+a)^4}{b}
$$
is integer and $a + b + c$ is prime.
$$
\frac{(a+b)^4}{c} + \frac{(b+c)^4}{a} + \frac{(c+a)^4}{b}
$$
is integer and $a + b + c$ is prime.