Question 121
Find all pairs $(a, b)$ of co-prime naturals such that $a \lt b$ and $b$ divides
$$
(n + 2)a^{n+1002} - (n + 1)a^{n+1001} - n a^{n+1000}
$$
for every natural number $n$.
$$
(n + 2)a^{n+1002} - (n + 1)a^{n+1001} - n a^{n+1000}
$$
for every natural number $n$.