Răspuns: Ai demonstrația mai jos
Explicație pas cu pas:
a)
[tex]\bf A = 3^{15}+3^{16} + 3^{17}[/tex]
[tex]\bf Dam~ factor~ comun~ pe~ 3^{15}[/tex]
[tex]\bf A = 3^{15}\cdot \big(3^{15-15}+3^{16-15} + 3^{17-15}\big)[/tex]
[tex]\bf A = 3^{15}\cdot \big(3^{0}+3^{1} + 3^{2}\big)[/tex]
[tex]\bf A = 3^{15}\cdot \big(1+3 + 9\big)[/tex]
[tex]\red{\underline{\bf A = 3^{15}\cdot 13 \implies A~\vdots~13}}[/tex]
b)
[tex]\bf B= 2^{22} +2^{24} +2^{26}[/tex]
[tex]\bf Dam~ factor~ comun~ pe~ 2^{22}[/tex]
[tex]\bf B = 2^{22}\cdot \big(2^{22-22}+2^{24-22} + 2^{26-22}\big)[/tex]
[tex]\bf B = 2^{22}\cdot \big(2^{0}+2^{2} + 2^{4}\big)[/tex]
[tex]\bf B = 2^{22}\cdot \big(1+4 + 16\big)[/tex]
[tex]\pink{\underline{\bf B = 2^{22}\cdot 21 \implies B ~\vdots~21}}[/tex]
Bafta multa !
