A number theory problem by Ralph Macarasig
Number Theory
Level
4
\[ \Large A =2017^{40^{640}} - 2017 \qquad \qquad B = 2017^{40^{544}} - 2017 \]
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 \(\overline{xy} = 1012\).
by
Ralph Macarasig