Problem 188
The hyperexponentiation of a number
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.
数的超幂
数a的正整数b次超幂或迭代幂次，记作a↑↑b或ba，按照如下方式递归定义：
a↑↑1 = a,
a↑↑(k+1) = a(a↑↑k).
举例来说，3↑↑2 = 33 = 27，因此3↑↑3 = 327 = 7625597484987，而3↑↑4约为103.6383346400240996*10^12。
求1777↑↑1855的最后8位数字。