Question

a)demonstrati ca numarul A=63^n+7^n+1x3^2n+1- 21^n x 3^n+2/ n€N este divizibil cu 13 b) demonstrati ca nr. B=35 pa n +7 la n×5la n+2 +3×7la n+1×5 la n/ n€N este divizibil cu 47

Answer 1

a) $A=63^n+7^{n+1}*3^{2n+1}- 21^n*3^{n+2}$
 $A=63^n+7^n*7*3^{2n}*3-21^n*3^{n}*3^2$
 $A=63^n+63^n*21- 63^n *9$
 $A=63^n(1+21-9)$
 $A=63^n*13~~este~divizibil~cu~13$  

b) $B=35^n +7^n*5^{n+2} +3*7^{n+1}*5^n$
$B=35^n +7^n*5^n*5^2+3*7^n*7*5^n$
$B=35^n +35^n*25+35^n*21$
$B=35^n(1+25+21)$
$B=35^n*47~~este~divizibil~cu~47$