un 2 00 4 Primitive root producing quadratics

Primitive Root Producing Quadratics

D.H. Lehmer found a quadratic polynomial such that 326 is a primitive root for the first 206 primes represented by this polynomial. It is shown that this is related to the class number one problem and prime producing quadratics. More impressive examples in the same spirit are given using recent results on prime producing quadratics. Y. Gallot holds the current record in which 206 is being repla...

A Priori Bounds for Some Infinitely Renormalizable Quadratics: I. Bounded Primitive Combinatorics

M ar 2 00 1 On primitive roots of unity , divisors of p 2 − 1 , and an extension to mod p 3 of Fermat ’ s Small Theorem

On primitive roots of unity, divisors of p 2 − 1, and an extension to mod p Abstract Primitive roots of 1 mod p k (k > 2 and odd prime p) are sought, in cyclic units group G k ≡ A k B k mod p k , coprime to p, of order (p − 1)p k−1. 'Core' subgroup A k has order p − 1 independent of precision k, and 'extension' subgroup B k of all p k−1 residues 1 mod p is generated by p+1. Integer divisors of ...

ar X iv : f un ct - a n / 94 06 00 5 v 2 2 4 Ju l 1 99 5 An Algebraic Spin and Statistics Theorem

A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional space-time. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebra...

On the robustness of primitive words

We investigate the e0ect on primitive words of point mutations (inserting or deleting symbols, substituting a symbol for another one), of morphisms, and of the operation of taking pre-xes. Several ways of producing primitive words are obtained in this framework. ? 2002 Elsevier Science B.V. All rights reserved.