Theo đề bài ta có:
\(n:7\) dư \(2\) nên \(n+5⋮7\)
\(n:8\) dư \(3\) nên \(n+5⋮8\)
\(n:9\) dư \(4\) nên \(n+5⋮9\)
\(\Rightarrow n+5\in BC\left(7;8;9\right)\)
\(BCNN\left(7;8;9\right)=504\)
\(BC\left(7;8;9\right)=B\left(504\right)=\left\{0;504;1008;...\right\}\)
\(\Rightarrow n\in\left\{-5;499;1003;...\right\}\)
Vì \(n\in N\) nên \(n\in\left\{409;1003;...\right\}\)