Greatest prime factor

$\begin{aligned} a & = 4^{19}-2^{34} \\ & = 2^{38}-2^{34} \\ & = 2^{34}(2^4-1) \\ & = 2^{34}(2^2-1)(2^2+1) \\ & = 2^{34}(3)(5) \end{aligned}$

Therefore, the greatest prime factor of $a$ is $\boxed{5}$ .

$4^{19}$ - $2^{34}$

= $2^{38}$ - $2^{34}$

= $2^{34}$ ( $2^{4}$ - 1)

= $2^{34}$ (16 - 1)

= $2^{34}$ x 15

= $2^{34}$ x 3 x 5

Answer is 5.

4^19 - 2^34 ^34 = 2^38 - 2^34 = (2^19 - 2^17)(2^19) + 2^17) = (2^17()4 - 1)(2^17)(4 + 1) = 3 * 5 *2^17, so greatest prime factor is 5.