Question 68
Find the sum of all positive integers $n$, $1 \leq n \leq 5000$, for which
$$
n^{2}+2475 n+2454+(-1)^{n}
$$
is divisible by $2477$. (Note that $2477$ is a prime number.)
$$
n^{2}+2475 n+2454+(-1)^{n}
$$
is divisible by $2477$. (Note that $2477$ is a prime number.)