Is it possible to find the units digit of
$2019^{2018^{2017^{.^{.^{.^{3^{2^{1}}}}}}}}$?
Where the expression contains all natural numbers $[1,2018]$ as powers and $2019$ as the main base.
Any help would be appreciated. THANKS!
The units digit of a power tower of consecutive numbers, from 2019 to 1
elementary-number-theoryexponentiationpower-towers
Best Answer
HINT
$2019\equiv -1\pmod{10}\Rightarrow 2019^a\equiv (-1)^a\pmod{10}$