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last two digits of a_9=9^{a_8}

Source: 1974 Swedish Mathematical Competition p3

March 26, 2021
number theoryrecurrence relationlast digitsDigits

Problem Statement

Let a1=1a_1=1, a2=2a1a_2=2^{a_1}, a3=3a2a_3=3^{a_2}, a4=4a3a_4=4^{a_3}, …\dots, a9=9a8a_9 = 9^{a_8}. Find the last two digits of a9a_9.
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