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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.

 Jul 28, 2024
 #1
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\(N\equiv 2 \pmod{LCM[6,7,8]}\\ N\equiv 2 \pmod{168}\)

 

set up equation

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

 

round down N = 6

 

 

answer is 6. 

 Jul 29, 2024
edited by BRAINBOLT  Jul 29, 2024

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