## The hyperexponentiation of a number

### Problem 188

Published on Friday, 4th April 2008, 02:00 pm; Solved by 4567; Difficulty rating: 35%The hyperexponentiation or tetration of a number a by a positive integer b, denoted by a↑↑b or ^{b}a, is recursively defined by:

a↑↑1 = a,

a↑↑(k+1) = a^{(a↑↑k)}.

Thus we have e.g. 3↑↑2 = 3^{3} = 27, hence 3↑↑3 = 3^{27} = 7625597484987 and 3↑↑4 is roughly 10^{3.6383346400240996*10^12}.

Find the last 8 digits of 1777↑↑1855.