6) Polynomial congruences and primitive roots Flashcards
1
Q
What is a polynomial congruence, and when is an integer a a solution to f(x) ≡ 0 mod n
A
2
Q
What can we say about solutions to f(x) ≡ 0 mod n
A
3
Q
What does the Chinese Remainder Theorem state
A
4
Q
What is the method for solving simultaneous congruences using the Chinese Remainder Theorem
A
5
Q
What does Lagrange’s Polynomial Congruence Theorem state
A
6
Q
What does Hensel’s lemma say about lifting solutions of polynomial congruences
A
7
Q
How do you lift a solution modulo p to p^m using Hensel’s lemma
A
8
Q
What is a primitive root modulo n
A
9
Q
What is the connection between primitive roots and the structure of Un
A
10
Q
How can you test if [a]∈Un is a primitive root modulo n
A
11
Q
How many elements of order d are there in Up, where p is prime
A
12
Q
When is Un cyclic
A
13
Q
What is Artin’s primitive root conjecture
A
