\[\frac{5n^{2} + 6n + 21}{n} =\]
\[= \frac{n(5n + 6) + 21}{n} =\]
\[= \frac{n(5n + 6)}{n} + \frac{21}{n} = 5n + 6 + \frac{21}{n}\]
\[\Longrightarrow n = 1;3;7;21.\]