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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
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
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 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
What is a primitive root? - Mathematics Stack Exchange Primitive roots are generators of the multiplicative group of integers modulo n n, which is useful in proofs Moreover primitive roots are difficult to compute in some groups, and cryptography takes advantage of this difficulty
Primitive polynomials - Mathematics Stack Exchange Anyway, between them, these eight elements have four distinct minimal polynomials (the conjugate of a primitive element is also primitive, and the conjugates come in pairs in a quadratic extension) The answer is thus that there are exactly 4 4 quadratic primitive polynomials