2) If is a prime and . Show that ( : is the Euler function)
3) a. Prove that is an integer if n is a prime and that it is not an integer
b. Prove that is not an integer if n is divisible by the square of a prime.
4) Prove Carmichael's conjecture for each ( mod 4)
(Carmichael conjectured that for each integer n, there exists an integer m n such that (n) = (m)
( : is the Euler function)
Please see the attached file for the fully formatted problems.
Mobius Functions, Euler Functions and Carmicheal's Conjecture are investigated. The solution is detailed and well presented.