CIIM 2010 Problem 5

Let $n,d$ be integers with $n,k > 1$ such that $g.c.d(n,d!) = 1$ . Prove that $n$ and $n+d$ are primes if and only if $$d!d((n-1)!+1) + n(d!-1) \equiv 0 \hspace{0.2cm} (\bmod n(n+d)).$$