Euler's Totient Theorem Problem 2 Solution
Revision as of 19:23, 23 April 2021 by Borealbear (talk | contribs) (Created page with "==Problem== (BorealBear) Find the last two digits of <math> 3^{3^{3^{3}}} </math>. ==Solution== This problem is just asking for <math> 3^{3^{3^{3}}}\pmod{100} </math>. We ca...")
Problem
(BorealBear) Find the last two digits of 
.
Solution
This problem is just asking for 
. We can start by expanding the uppermost exponent, which gives us 
. Then, since 
, the exponent will be equal to 
. We can see that 
, so the expression simplifies to 
.
We're now left with finding the last two digits of 
. To do this, we use Chinese Remainder Theorem. We find that it is 
mod 
and 
mod 
From here, we use guess+check to get 
.
