## Problem of the Day #41: Last Digits of an Exponentiated FactorialApril 29, 2011

Posted by Albert in : potd , trackback

Albert is mad at everyone for stipulating the so-called “Albert week” on MPOTD. To get his revenge, he makes everyone else work on the following problem:

1. Prove that there exists a function $g(k)$ such that the last $k$ digits of $f(n) = 2^{n!}$ becomes constant for all $n \geq g(k)$.
2. Find the smallest integer $m$ such that the last $32$ digits of $f(n)$ are constant for all $n \geq m$.