The Agony of Extraordinarily Huge numbers

Number Theory Level 5

\[\huge 19^{17^{15^{\cdots^{3^{1}}}}}\]

Find the last \(2\) digits of the above number.

Details and Assumptions:

The powers of the next preceding number decreases by \(2\) starting from \(17\) and ending off with \(1\).

Also, this question is taken from a local Mathematics competition.(Singapore)

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