2. It is known that $n^{2012}+n^{2010}$ is divisible by 10 for some positive integer $n$. Which of the following numbers is not a possible value for $n$ ?
(A) 2 ;
(B) 13 ;
(C) 35 ;
(D) 47 ;
(E) 59 .
2. Answer: (E).
Note that $n^{2012}+n^{2010}=n^{2010}\left(n^{2}+1\right)$.
If $n=2$, then $5\left(n^{2}+1\right)$ and $2 n^{2010}$. If $n=13$ or 47 , then $10\left(n^{2}+1\right)$.
If $n=35$, then $2 \quad\left(n^{2}+1\right)$ and $5 n^{2010}$. If $n=59$, then $5 \nmid\left(59^{2}+1\right)$ and $5 \nmid n^{2010}$.