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Problem of the Day #41: Last Digits of an Exponentiated Factorial April 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 $n \geq m$.

Comments»

1. Aziz - April 29, 2011

cool story bro