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- 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?
- 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
- Understanding the definition of primitive recursion.
Primitive recursion does allow the "next-step-provider" h h to see both inputs and the previous value, but we don't need to use that information In most natural examples I think we don't in fact need that Finally, it may also help to go in the opposite direction: given a g g and h h, try to compute the first few values of the resulting f f
- What is a primitive root? - Mathematics Stack Exchange
Primitive roots are generators of the multiplicative group of integers modulo n, which is useful in proofs Moreover primitive roots are difficult to compute in some groups, and cryptography takes advantage of this difficulty
- What is a primitive polynomial? - Mathematics Stack Exchange
9 What is a primitive polynomial? I was looking into some random number generation algorithms and 'primitive polynomial' came up a sufficient number of times that I decided to look into it in more detail I'm unsure of what a primitive polynomial is, and why it is useful for these random number generators
- Practical method of calculating primitive roots modulo a prime
As others have mentioned, we don't know efficient methods for finding generators for (Z pZ)∗ (ℤ p ℤ) ∗ without knowing the factorization of p − 1 p − 1 However, you can efficiently generate a random factored number n n, then test if n + 1 n + 1 is prime, and then compute primitive roots modulo n + 1 n + 1 See Victor Shoup -- A Computational Introduction to Number Theory and
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