Number Theory and Cryptography
Practice Midterm 2 (3/31)
Choose seven problems from the list below; each problem is worth 14 points. Please show all work; for
true/false problems, give a proof or a counterexample. As usual, p denotes a prime.
1. True or F

Number Theory and Cryptography
Homework 4 (due 2/17) (with solution for problem
5)
1. a) Prove that 5 is a generator of Z
23 .
b) Find all generators of Z
,
and
express
each of them as a power of 5.
23
2. Prove that 11 is a generator of Z
73 .
3. Let p be

Number Theory and Cryptography
Practice Problems, Batch 1, with sketched solutions
For true/false problems, give a proof or a counterexample. As usual, p denotes a prime.
1. True or False: x6 1 has six roots in Z61 .
Solution: True, because 6|60 = (61).
2