Calculate the Last 2 Digits of a Tower of Powers in Number Theory

This is a tutorial on Number Theory and how to Find the last 2 digits of 7^(7^7)
Best place to start is with the (7^7) .
Use Eulers Totient Function to find 7^7 is congruent to alpha mod phi(100) = 40 , then phi(40)=16.
phi(100) = phi(25)*phi(4) which is in the form of phi(p^a)=p^(a-1)(p-1)
We use this technique again for phi(40)= phi(8)*phi(5) =16
We then are left with 7^7 mod 16 which is 7.
The final part is to find 7^7 mod 100 which is 43.
#algebra
#euclidsalgorithm
#euclid_division_algorithm
#euclidsdivisionlemma
#euclidean
#mathtricks
#numbersystem
#numbers
#numbertheory
#bernoulli

[Man-qqvm]

Good. Can have method to find 3th or n-th digit ?