help with mods

Question

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+2729

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.

LiIIiam0216 Jul 28, 2024

BRAINBOLT · Answer 1 · 2024-07-29T05:00:35

$N\equiv 2 \pmod{LCM[6,7,8]}\\ N\equiv 2 \pmod{168}$

set up equation

$168N+2=1000\\ 168N=998\\ N=\frac{499}{84} \approx 5.940$

round down N = 6

answer is 6.