Euler's Totient Theorem Problem 2 Solution
Revision as of 17:42, 21 March 2023 by Megaboy6679 (talk | contribs)
Problem
(BorealBear) Find the last two digits of .
Solution
Finding the last two digits is equivalent to finding . We can start by expanding the uppermost exponent:
. Then, since
, the exponent is equal to
. We see that
, so it simplifies to
.
We now just need to find the last two digits of . Using the Chinese Remainder Theorem, we find that the last two digits are
and
. We guess and check to get
.
~BorealBear
Link back to Euler's Totient Theorem.