Question

aratati ca nr A=7*12 la n*3 la n+1+6*4 la n+1*9 la n+2+18 la n+1*2la n+1 este divizibil cu 2001,oricare ar fi n apartine lui N stelat

Answer 1

$A = 7*12^n*3^{n+1}+6* 4^{n+1} * 9^{n+2} + 18^{n+1} *2^{n+1}$

$A = 7*3^n*4^n*3^n*3+6* 4^n*4 * 9^n*9^2+ 18^n*18 *2^n*2$

$A = 7*3^{2n}*4^n*3+6* 4^n*4 * 3^{2n}*9^2+ 2^n*9^n*18 *2^n*2$

$A = 7*3^{2n}*2^{2n}*3+6* 2^{2n}*4 * 3^{2n}*9^2+ 2^{2n}*3^{2n}*18 *2$

$A = 3^{2n}*2^{2n}*(7*3+6* 4 * 9^2+ 18 *2)$

$A = 3^{2n}*2^{2n}*(21+1944+ 36)$

$A = 3^{2n}*2^{2n}*2001$       este divizibil cu 2001