8. Let $n=\left(2^{4}-1\right)\left(3^{6}-1\right)\left(5^{10}-1\right)\left(7^{12}-1\right)$. Which of the following statements is true?
(A) $n$ is divisible by 5,7 and 11 but not 13;
(B) $n$ is divisible by 5,7 and 13 but not 11;
(C) $n$ is divisible by 5,11 and 13 but not 7;
(D) $n$ is divisible by 7,11 and 13 but not 5 ;
(E) None of the above.
8. Answer: (E).
Since $5\left|\left(2^{4}-1\right), 7\right|\left(3^{6}-1\right), 11\left|\left(5^{10}-1\right), 13\right|\left(7^{12}-1\right), n$ is divisible by $5,7,11$ and 13 .