Find the integer $n$, $0 \le n \le 7$, such that \[n \equiv -3737 \pmod{8}.\]
To find $n$, I need to find a multiple of $8$ that is close to $-3737$, and then see what the difference is. I can use long division or a calculator to find that $-3737 \div 8 = -467.125$. This means that $-3737 = -467 \times 8 - 1$, or in other words, $-3737 \equiv -1 \pmod{8}$. Therefore, $n$ must be the same as $-1$ in modulo $8$, which is the same as $7$. So, $n = 7$. 