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What are primitive roots modulo n? - Mathematics Stack Exchange I'm trying to understand what primitive roots are for a given mod n mod n Wolfram's definition is as follows: A primitive root of a prime p p is an integer g g such that g (mod p) g (mod p) has multiplicative order p − 1 p 1 The main thing I'm confused about is what "multiplicative order" is Also, for the notation g (mod p) g (mod p), is it saying g g times mod p mod p or does it have
Finding a primitive root of a prime number How would you find a primitive root of a prime number such as 761? How do you pick the primitive roots to test? Randomly? Thanks
Product of two primitive polynomials - Mathematics Stack Exchange The part "fg f g primitive f f and g g primitive" is the trivial part both you and the question deal with If f f or g g would be divisible be a non-unit in R R, then so would fg f g, that's all The question is about the other direction, which is Gauss's lemma
Find all the primitive roots of - Mathematics Stack Exchange Find all the primitive roots of 13 13 My attempt: Since that 13 13 is a prime I need to look for g g such that g13−1 ≡ 1 (mod 13) g 13 1 ≡ 1 (mod 13) There are ϕ(12) = 4 ϕ (12) = 4 classes modulo 12 12 how can I find the classes?
The primitive $n^ {th}$ roots of unity form basis over $\mathbb {Q . . . Suppose the primitive nth n t h roots of unity, denoted {1,η(1) n, …,η(k−1) n} {1, η n (1),, η n (k 1)} do not form a basis for the cyclotomic field of nth n t h roots of unity over Q Q (this could either mean the primitive roots either don't span or are not linearly independent; intuition guides me to suspect that somehow we can infer
Proof of existence of primitive roots - Mathematics Stack Exchange In my book (Elementary Number Theory, Stillwell), exercise 3 9 1 asks to give an alternative proof of the existence of a primitive root for any prime Let p p be prime, and consider the group Z pZ Z p Z