17) If it is known that the number $2^{48}-1$ has exactly two divisors between 60 and 70. Which are they?
(A) 61 and 63
(B) 61 and 65
(C) 63 and 65
(D) 61 and 67
(E) 63 and 69
17) The answer is (C)

The factors 63 and 65 are certainly present because

$2^{48}-1=\left(2^{24}+1\right)\left(2^{24}-1\right)=\left(2^{24}+1\right)\left(2^{12}+1\right)\left(2^{12}-1\right)=\left(2^{24}+1\right)\left(2^{12}+1\right)\left(2^{6}+1\right)\left(2^{6}-1\right)$

and $2^{6}-1=63,2^{6}+1=65$.