22.
b)sunt 62 de termeni
1+[tex] 3^{1}=4; 3^{2}+ 3^{3}= 3^{2}*4;....; 3^{60}+ 3^{61}= 3^{60}*4[/tex]
In concluzie B=4*([tex] 1+ 3^{2}+....+ 3^{60}[/tex]⇒B divizibil
cu 4
c)sunt 72 de termeni
[tex] 1+2^{1}+2^{2}+2^{3}=15 [/tex];[tex]2^{4}+2^{5}+2^{6}+2^{7}=2^{4}*15;....;2^{68}+2^{69}+2^{70}+2^{71}=2^{68}*15
[/tex]
C=[tex]15*(1+2^{4}+...+2^{68})=>C=3*5(1+2^{4}+...+2^{68})=>C[/tex]
divizibil cu 5
26.b)
B=[tex]7^{n}*5^{n}+7^{n}*5^{n}*25+3*7^{n}*7*5^{n}[/tex]
B=[tex]7^{n}*5^{n}*(1+25+21)[/tex]⇒B=[tex]7^{n}*5^{n}*47[/tex]⇒B
divizibil cu 47
c)A=[tex]7*12^{n}*3^{n}*3+6*4^{n}*4*9^{n}*81+18^{n}*18*2^{n}*2[/tex]
A=[tex]36^{n}*21+36^{n}*1944+36^{n}*36[/tex]
A=[tex]36^{n}*(21+1944+36)=>A=36^{n}*2001=>A[/tex] divizibil cu 2001
