project_euler.problem_188.sol1

Project Euler Problem 188: https://projecteuler.net/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 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 103.6383346400240996*10^12.

Find the last 8 digits of 1777↑↑1855.

References:

• https://en.wikipedia.org/wiki/Tetration

Functions

_modexpt(→ int)	Returns the modular exponentiation, that is the value
solution(→ int)	Returns the last 8 digits of the hyperexponentiation of base by

Module Contents

project_euler.problem_188.sol1._modexpt(base: int, exponent: int, modulo_value: int) → int

Returns the modular exponentiation, that is the value of base ** exponent % modulo_value, without calculating the actual number. >>> _modexpt(2, 4, 10) 6 >>> _modexpt(2, 1024, 100) 16 >>> _modexpt(13, 65535, 7) 6

project_euler.problem_188.sol1.solution(base: int = 1777, height: int = 1855, digits: int = 8) → int

Returns the last 8 digits of the hyperexponentiation of base by height, i.e. the number base↑↑height:

>>> solution(base=3, height=2)
27
>>> solution(base=3, height=3)
97484987
>>> solution(base=123, height=456, digits=4)
2547