MathDB
Spring Round (2012) #5

Source:

December 3, 2012

Problem Statement

Let a↑↑b=aaa…aa{ a\uparrow\uparrow b = {{{{{a^{a}}^a}^{\dots}}}^{a}}^{a}} , where there are b b a's in total. That is a↑↑b a\uparrow\uparrow b is given by the recurrence a↑↑b={ab=1aa↑↑(b−1)b≥2 a\uparrow\uparrow b = \begin{cases} a & b=1\\ a^{a\uparrow\uparrow (b-1)} & b\ge2\end{cases} What is the remainder of 3↑↑(3↑↑(3↑↑3)) 3\uparrow\uparrow( 3\uparrow\uparrow ( 3\uparrow\uparrow 3)) when divided by 60 60 ?
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