Question

Scrieti numarul 2011 ca o diferenta de petrate de numere naturale dau 30 puncte

Answer 1

[tex]2011= a^{2} - b^{2}.~Folosim~ formula~a^{2} - b^{2}=(a+b)\cdot(a-b). \\ Deci,~2011=(a+b)\cdot(a-b).~Cum~2011~este~prim\Rightarrow \\ a+b=2011 \\ a-b=1\Rightarrow~a=b+1\Rightarrow2b+1=2010\Rightarrow \underline{b=1005},~\underline{a=1006.} \\ In~concluzie,~\boxed{2011=1006 ^{2} -1005 ^{2}.} [/tex]