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JOMO 7, Long 2

Ronald is playing around with arrow notation to denote exponentiation, where \(a\uparrow b=a^b\). For example, \(2\uparrow2=2^2=4 \) and \(3\uparrow4=3^4=81\)

A "double arrow" is used for iterated exponentiation, as seen in the following: \[a\uparrow\uparrow b = \underbrace{a^{a^{\ldots^a}}}_{b\text{ copies of }a}.\] For example, \[2\uparrow\uparrow3=2^{2^2}=2^4=16.\]

You can use this information to extend the following. \[a\uparrow\uparrow b=a^{a\uparrow\uparrow(b-1)}\] Find, with proof, the last digit of \(3\uparrow\uparrow 2014\).

Note by Aditya Raut
2 years, 1 month ago

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