Establish the following properties of the Euler function , (a) If p is prime and n >

Establish the following properties of the Euler function φ, 

(a) If p is prime and n > 0, then φ(pⁿ) = pⁿ(1- 1/p) = pⁿ(1-1/p).

(b) If (m, n) = 1, then φ(mn) = φ(m)φ(n). 

(c) If n = p₁^k1. • •p_r^kr (p_i distinct primes; k_i > O), then φ(n) = n(1 - 1/p₁) (1 - 1/p₂)· · ·(1 - 1/p_r). 

(d) 

(e) 

Transcribed Image Text:

Σφ(α) = n. dẫn