## Remainder of a power tower under modulo $2013$

I have an expression like this: $$\left(\large 6000^{5999^{5998^{5997^{{\ldots^{1}}}}}}\right)\bmod 2013$$ Then which method should I use to solve it? Please provide the method not the answer. Editor’s Note: Note that this is a power tower with different values and not the same value as with general tetration. Also, don’t confuse tetration with exponentiation. Both are completely … Read more