Raspuns: Ai demonstrația mai jos
Salutare!
[tex]\bf A = 9\cdot2^{n+2} \cdot5^{n+1} +10^{n+2} -3\cdot2^{n+1} \cdot 5^{n+2}[/tex]
[tex]\bf A = 3^{2}\cdot2^{n+2} \cdot5^{n+1} +2^{n+2}\cdot5^{n+2} -3\cdot2^{n+1} \cdot 5^{n+2}[/tex]
[tex]\bf A = 2^{n+1}\cdot 5^{n+1} \cdot \big(3^{2}\cdot2^{1} +2^{1}\cdot5^{1} -3\cdot 5^{1} \big)[/tex]
[tex]\bf A = 2^{n+1}\cdot 5^{n+1} \cdot \big(9\cdot2 +10-3\cdot 5 \big)[/tex]
[tex]\bf A = 2^{n+1}\cdot 5^{n+1} \cdot \big(18 +10-15 \big)[/tex]
[tex]\bf A = 2^{n+1}\cdot 5^{n+1} \cdot 13 \implies \red{A ~\vdots~ 13,~pentru~ \forall~n\in\mathbb{N}}[/tex]
Bafta multa !
