[tex]\text{Daca $n$ este par atunci $n=2k$}\\
2^{2k}\cdot5^{2k+1}=2^n\cdot5^{2k}\cdot5=10^{2k}\cdot5=10^{2k}(1+4)=10^{2k}+10^{2k}\cdot2^2\\
=(10^k)^2+(2\cdot10^k)^2\\
\text{Daca $n$ este impar atunci $n=2k+1$}\\
2^{2k+1}\cdot5^{2k+2}=2^{2k}\cdot5^{2k}\cdot2\cdot5^2=2^{2k}\cdot5^{2k}\cdot50=\\
2^{2k}\cdot5^{2k}\cdot(1+49)=2^{2k}\cdot5^{2k}\cdot1+2^{2k}\cdot5^{2k}\cdot49=\\
=(10^k)^2+(7\cdot10^k)^2
[/tex]
