Let p be a prime. = 0 for 0 0 and gcd (p, b) = 1....

 

Transcribed Image Text:

Let p be a prime. = 0 for 0 0 and gcd (p, b) = 1. 1+cph+1 with gcd(p, c) = 1, unless p = 2 and h = 1. ap [10 pts] Show that: If p is odd and e> 0, then: (c) In (Zpe), [1 + p] has order pe-1; ->. and [15 pts] (d)(Zpe) is cyclic. [15 pts] (e)... For e> 2, (Ze){[1]} , and.... [5] = [14] has order 2e-2. -> [15 pts] Let p be a prime. = 0 for 0 0 and gcd (p, b) = 1. 1+cph+1 with gcd(p, c) = 1, unless p = 2 and h = 1. ap [10 pts] Show that: If p is odd and e> 0, then: (c) In (Zpe), [1 + p] has order pe-1; ->. and [15 pts] (d)(Zpe) is cyclic. [15 pts] (e)... For e> 2, (Ze){[1]} , and.... [5] = [14] has order 2e-2. -> [15 pts]