Problem 2CE

Exercise 1. This software lists all idempotents (see the chapter exercises for the definition) in Z n . Run the program for various values of n . Use these data to make conjectures about the number of idempotents in Z n as a function of n. For example, how many idempotents are there when n is a prime power? What about when n is divisible by exactly two distinct primes? In the case where n is of the form pq where p and q are primes can you see a relationship between the two idempotents that are not 0 and 1? Can you see a relationship between the number of idempotents for a given n and the number of distinct prime divisors of n ?Exercise 2. This software lists all nilpotent elements (see the chapter exercises for definition) in Z n . Run your program for various values of n . Use these data to make conjectures about nilpotent elements in Z n as a function of n .Exercise 3. This software determines which rings of the form Z p [ i ] are fields. Run the program for all primes up to 37. From these data, make a conjecture about the form of the primes that yield a field.Exercise 1. This software lists all idempotents (see the chapter exercises for the definition) in Z n . Run the program for various values of n . Use these data to make conjectures about the number of idempotents in Z n as a function of n. For example, how many idempotents are there when n is a prime power? What about when n is divisible by exactly two distinct primes? In the case where n is of the form pq where p and q are primes can you see a relationship between the two idempotents that are not 0 and 1? Can you see a relationship between the number of idempotents for a given n and the number of distinct prime divisors of n ?Exercise 2. This software lists all nilpotent elements (see the chapter exercises for definition) in Z n . Run your program for various values of n . Use these data to make conjectures about nilpotent elements in Z n as a function of n .Exercise 3. This software determines which rings of the form Z p [ i ] are fields. Run the program for all primes up to 37. From these data, make a conjecture about the form of the primes that yield a field.

SEPTEMBER 6, 2 017 ● STEPS T O ESEARCH PROCESS ○ The communication research process can be viewed as an ongoing cycle of nterrelate hases of research activities: ■ Conceptualization ■ Planning ■ Methods/Data Collection ■ Analyze he data ■ Reconceptualization ○ STEP 1: ONCEPTUALIZATION ■ Forming an dea about what needs to be studied ● Starts with experiences, observations, abstract) ● Identify ○ Topic (ideally communication-based) ○ Relevant literature: What is known What