Question 16: Let \(\begin{array}{l} A = – 13{x^{17}}{y^{2n – 3}} + 22{x^{16}}{y^7};B = – 7{x^{3n + 1}}{y^6} \end{array}\). Find the natural number n so that polynomial A is divisible by monomial B.

\(\begin{array}{l} A = – 13{x^{17}}{y^{2n – 3}} + 22{x^{16}}{y^7};B = – 7{ x^{3n + 1}}{y^6}\\ {\rm{A}} \vdots {\rm{B}} \Leftrightarrow \left\{ \begin{array}{l} n \in N\ \ 2{\rm{n}} – 3 \ge 6\\ 16 \ge 3{\rm{n}} + 1 \end{array} \right. \Leftrightarrow n = 5 \end{array}\)