11. What is the greatest prime factor of $3^{12}-1$?
(A) 73
(B) $3^{6}+1$
(C) 107
(D) 13
(E) 949
Problem 11. The answer is (A).

Since $3^{12}-1=\left(3^{6}-1\right)\left(3^{6}+1\right)=728 \cdot 730$, it is easy to arrive at the factorization:

$$
3^{12}-1=\left(2^{3} \cdot 7 \cdot 13\right) \cdot(2 \cdot 5 \cdot 73)=2^{4} \cdot 5 \cdot 7 \cdot 13 \cdot 73
$$

thus the largest prime factor of $3^{12}-1$ is 73.

(Problem proposed by R. Zanotto)