Vì n chia cho 17 dư 8 \(\Rightarrow n+9⋮17\)
Vì n chia cho 25 dư 16 \(\Rightarrow n+9⋮25\)
\(\Rightarrow n+9\in BC\left(17;25\right)\)
Ta có:
\(17=17\)
\(25=5^2\)
\(\Rightarrow BCNN\left(17;25\right)=17.5^2=425\)
\(\Rightarrow BC\left(17;25\right)=B\left(425\right)=\left\{0;425;850;1275;...\right\}\)
\(\Rightarrow n+9\in\left\{0;425;850;1275;...\right\}\)
\(\Rightarrow n\in\left\{416;841;1266;...\right\}\)
Vậy \(n\in\left\{416;841;1266;...\right\}\)
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