منابع مشابه
Primitive Roots in a Finite Field
with minimum m such that a(y) =0; 7 is said to belong to a(x). In particular if a(x) =xp" — x, Ore calls 7 a primitive root. It is easy to see that the two varieties of primitive roots are not identical; for example in the GF{21) defind by 04+0+l, 0 is a primitive root in the original sense but not in Ore's sense (since it belongs tox*-\-xi-\-x2-\-x). On the other hand it can be verified that 8...
متن کاملOn Finding Primitive Roots in Finite Fields
We show that in any finite field Fq a primitive root can be found in time O(q’ ‘+’ ) Let Fq denote a finite field of q elements. An element 0 E IFq is called a primitive root if it generates the multiplicative group F;,“. We show that a combination of known results on distribution primitive roots and the factorization algorithm of [6] leads to a deterministic algorithm to find a primitive root ...
متن کاملOn simultaneous primitive roots
Given finitely many non zero rational numbers which are not ±1, we prove, under the assumption of Hypothesis H of Schinzel, necessary and sufficient conditions for the existence of infinitely many primes modulo which all the given numbers are simultaneously primitive roots. A stronger result where the density of the primes in consideration was computed was proved under the assumption of the Gen...
متن کاملFibonacci Primitive Roots
(1) g 2 = g + 1 (mod p). It i s obvious that if (1) holds then so do (2) g 3 = g 2 + g (mod p) , (3) g 4 = g 3 + g 2 (mod p) , e t c .
متن کاملLucas Primitive Roots
is called the characteristic polynomial of the sequence U. In the case where P = -g = 1, the sequence U is the Fibonacci sequence and we denote its terms by F0, Fl9 F2, ... . Let p be an odd prime with p\Q and let e > 1 be an integer. The positive integer u = u(p) is called the rank of apparition of p in the sequence U if p\Uu and p\Um for 0 < m < u; furthermore, u = u(p) is called the period o...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1952
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1952-0051869-9