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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
3 years, 4 months ago

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