Question 13
Find all the triples of integers $(a,b,c)$ such that the number
$$
N = \frac{(a-b)(b-c)(c-a)}{2} + 2
$$
is a power of $2016$.
(A power of $2016$ is an integer of the form $2016^n$, where $n$ is a non-negative integer).
$$
N = \frac{(a-b)(b-c)(c-a)}{2} + 2
$$
is a power of $2016$.
(A power of $2016$ is an integer of the form $2016^n$, where $n$ is a non-negative integer).