Question

Aratati ca numarul N=2×7 la puterea n+2 -3×7 la puterea n+1 +7 la puterea n divizibil cu39

Answer 1

 

$\displaystyle \bf\\N=2\times7^{n+2}-3\times7^{n+1}+7^n=\\=2\times7^n\times7^2-3\times7^n\times7^1+7^n=\\=7^n(2\times7^2-3\times7^1+1)=\\=7^n(2\times49-3\times7+1)=\\=7^n(98-21+1)=\\=7^n\times78\\N=7^n\times2\times39~\vdots~39~~\text{(deoarece unul din factori este 39)}$