Primitive Root Producing Quadratics

un 2 00 4 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

Root-Labeling

In 2006 Jambox, a termination prover developed by Endrullis, surprised the termination community by winning the string rewriting division and almost beating AProVE in the term rewriting division of the international termination competition. The success of Jambox for strings is partly due to a very special case of semantic labeling. In this paper we integrate this technique, which we call root-l...

A Simple Procedure for Extracting Quadratics from a given Algebraic

Any linear time-invariant continuous or discrete system can be represented either in terms of characteristic algebraic polynomial or in the form of open-loop transfer function. The open-loop transfer function will consist of numerator polynomial and denominator polynomial. To understand the transient characteristics of the system, the denominator polynomial is analysed for its roots. Any n orde...

Cumulative Chords, Piecewise-quadratics and Piecewise-cubics

Cumulative chord piecewise-quadratics and piecewise-cubics are examined in detail, and compared with other low degree interpolants for unparameterized data from regular curves in , especially piecewise-4-point quadratics. Orders of approximation are calculated and compared with numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data. This work ...