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Primitive polynomials - Mathematics Stack Exchange A polynomial is called primitive (in the context of finite fields), iff its zero is a generator of the multiplicative group of the field it generates In this case the polynomial is quadratic, so a root α will generate the field L = F25 The multiplicative group of L is cyclic of order 24 By the well known facts about cyclic groups, the group
Find all the primitive roots of - Mathematics Stack Exchange Primes have not just one primitive root, but many So you find the first primitive root by taking any number, calculating its powers until the result is 1, and if p = 13 you must have 12 different powers until the result is 1 to have a primitive root If you tried a number a that wasn't a primitive root then don't try it's powers but some other
linear algebra - Primitive matrices - Mathematics Stack Exchange A square matrix P ⩾ 0 P ⩾ 0 is called primitive if there exists a power k k such that Pk> 0, P k> 0, that is, there exists a k k such that for all ij, i j, the entries ij i j are positive I read it in the Internet but it was not referenced linear-algebra matrices Share
Primitive roots of $25$ - Mathematics Stack Exchange For example, 2 is a primitive root of 25, since it cycles through all of the twenty possible answers before returning to 1 On the other hand, 7 is not, because it only cycles through just four values (7, 24, 18, 1) There are a smattering of primes where the smallest primitive root of p is not a primitive root of p^2, but they're pretty rare
$fg$ primitive $\\to$ $f, g$ primitive - Mathematics Stack Exchange Therefore, if fg f g is primitive, K = (1) K = (1) and thus I ⋅ J = (1) I ⋅ J = (1) Now the only step would be to show that this implies I = (1) I = (1) and (J) = 1 (J) = 1 However, I am stuck here, how do I go about proving this? Obviously, I ⊃ K I ⊃ K and J ⊃ K J ⊃ K K ⊆ IJ ⊆ IA = I, K ⊆ IJ ⊆ AJ = J, K ⊆ I J ⊆ I A
Uniqueness of Primitive of an integral - Mathematics Stack Exchange The existence is not difficult to see by using the fact that f f is continuous and therefore by fundamental theorem of calculus, we obtain F F as the primitive of f f Moreover, if another primitive G G exists, then ∀x ∈ I, F(x) − G(x) = C ∀ x ∈ I, F (x) − G (x) = C (constant) Now, my problem is I want to show that C = 0 C = 0 by