Question

aratati ca numarul n=2 la 30+2 la 31+2la 32+2la 33 este divizibil cu 15 va rogg​

Answer 1

 

$\displaystyle\bf\\n=2^{30}+2^{31}+2^{32}+2^{33}\\\\n=2^{30+0}+2^{30+1}+2^{30+2}+2^{30+3}\\\\n=2^{30}\times2^0+2^{30}\times2^1+2^{30}\times2^2+2^{30}\times2^3\\\\n=2^{30}(2^0+2^1+2^2+2^3)\\\\n=2^{30}(1+2+4+8)\\\\n=2^{30}\times15\\\\n~\vdots~15~deoarece~are~un~factor~egal~cu~15$