# The hyperexponentiation of a number

*Author: Shlomi Fish*

https://projecteuler.net/problem=188

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.

Source code: prob188-shlomif.pl

use v6; sub hyperexp_modulo(int $base, int $exp, int $mod) returns int { if $exp == 1 { return ($base % $mod); } my Int $mod1 = $base; my Int $e = 1; while $mod1 != 1 { ($mod1 *= $base) %= $mod; $e++; } my int $mod_recurse = hyperexp_modulo($base, $exp - 1, $e); return $base.expmod($mod_recurse, $mod); } printf "%08d\n", hyperexp_modulo(1777, 1855, 100_000_000);