## The hyperexponentiation of a number

### Problem 188

Published on Friday, 4th April 2008, 02:00 pm; Solved by 3547

The hyperexponentiation or tetration of a number a by a positive integer b, denoted by a↑↑b or ba, is recursively defined by:
a↑↑1 = a,
a↑↑(k+1) = a(a↑↑k).

Thus we have e.g. 3↑↑2 = 33 = 27, hence 3↑↑3 = 327 = 7625597484987 and 3↑↑4 is roughly 103.6383346400240996*10^12.

Find the last 8 digits of 1777↑↑1855.