Quiz # 8 for Dr. Z.’s Number Theory Course for Nov. 14, 2013

NAME: (print!) E-MAIL ADDRESS: (print!)

1. (i) (2 pts.) Define σ_{2}(n) (ii) (2 pts.) State the formula for σ_{2}(n) in terms of the expression of n as a product of prime powers (iii) (2 pts.) Verify it for n = 15 by using the definition and the formula

2. (4 pts.) Prove that if p is a prime, and 2^{p} − 1 is also a prime, then 2^{p−1} · (2^{p} − 1)

is a perfect number.