Euler's Totient Theorem Problem 2 Solution
(BorealBear) Find the last two digits of .
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.