A number theory problem by Ralph Macarasig

Number Theory Level 3

$\Large A =2017^{40^{640}} - 2017 \qquad \qquad B = 2017^{40^{544}} - 2017$

The greatest common divisor of $A$ and $B$ can be expressed in the form $\large 2017^{x^{y}} - 2017$ , where $x$ and $y$ are integers.

Submit your answer as $\overline{xy}$ , which is the concatenation of the digits of $x$ and $y$ . For example, if $x = 10$ and $y = 12$ , then $\overline{xy} = 1012$ .

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