Explicație pas cu pas:
[tex]A = 9 \times {2}^{n} \times {15}^{n + 1} - 3 \times {6}^{n} \times {5}^{n + 2} - 7 \times {3}^{n + 1} \times {10}^{n} \\ [/tex]
[tex]= 9 \times {2}^{n} \times 15 \times {(3 \times 5)}^{n} - 3 \times {(2 \times 3)}^{n} \times {5}^{2} \times {5}^{n} - 7 \times 3 \times {3}^{n} \times {(2 \times 5)}^{n} \\ [/tex]
[tex]= 135 \times {2}^{n} \times {3}^{n} \times {5}^{n} - 75 \times {2}^{n} \times {3}^{n} \times {5}^{n} - 21 \times {3}^{n} \times {2}^{n}\times {5}^{n} \\ [/tex]
[tex]= \times {2}^{n} \times {3}^{n} \times {5}^{n} \times (135 - 75 - 21) \\ [/tex]
[tex]= {2}^{n} \times {3}^{n} \times {5}^{n} \times 39 \\ [/tex]
[tex]= {2}^{n} \times {3}^{n} \times {5}^{n} \times 3 \times 13[/tex]
→ numărul A este divizibil cu 13, pentru orice n ∈ N
