Find the number of solutions to N &\equiv 2 \pmod{6}, \\ N &\equiv 2 \pmod{7}, \\ N &\equiv 2 \pmod{8} in the interval 0 \le N < 1000.
\(N\equiv 2 \pmod{LCM[6,7,8]}\\ N\equiv 2 \pmod{168}\)
set up equation
\(168N+2=1000\\ 168N=998\\ N=\frac{499}{84} \approx 5.940\)
round down N = 6
answer is 6.
+2651 
