[tex]A=72^{n+1}+3^{2n+1}*2^{3n+2}+3^{2n}*2^{3n}*6 [/tex]
[tex]A=72^n*72+3^{2n}*3*2^{3n}*2^2+3^{2n}*2^{3n}*6[/tex]
[tex]A=2^{3n}*3^{2n}(72+3*4+6)[/tex]
[tex]A= 2^{3n}*3^{2n}*90[/tex]
[tex]A=2^{3n}*3^{2n}*6*15[/tex] este divizibil cu 15
[tex]B=7^{n+2}*5^{n+1}*3^{n+1}-735 [/tex]
[tex]B=7^{n}*7^2*5^{n}*5*3^{n}*3-735 [/tex]
[tex]B=7^{n}*5^{n}*3^{n}*49*5*3-735 [/tex]
[tex]B=(7*5*3)^{n}*735-735 [/tex]
[tex]B=105^{n}*735-735 [/tex]
[tex]B=735*(105^{n}-1) [/tex]
[tex]105^{n} [/tex] are ultima cifra 5, (un numar ce are ultima cifra 5, ridicat la orice putere va da un numar ce va avea aultima cifra 5 )
=> [tex]105^{n}-1= \frac{}{n5} -1= \frac{}{n4} [/tex]
un numar ce are ultima cifra 4 este divizibil cu 2
=> [tex]105^{n}-1= k*2[/tex]
=>B= 735*k*2
B= k*1470 este divizibil cu 1470
