Question

aratati ca nr A= 3*2 (la n) + 2 la (n+1) + 5*2 la (n+1) +2la (n +3)este divizibil cu 23 oricare ar fi n

Answer 1

[tex]A=3\cdot 2^n+2^{n+1}+5\cdot 2^{n+1}+2^{n+3}\\ A=3\cdot 2^n+2^n\cdot 2+5\cdot 2^n\cdot 2+2^n\cdot 8\\ A=2^n(3+2+5\cdot 2+8)\\ A=2^n(13+10)\\ A=2^n\cdot 23 \vdots\ 23.[/tex]