In this paper, using a method of Luca and the author, we find all values x such that the quadratic polynomials x + 1, x + 4, x + 2 and x − 2 are 200-smooth and all values x such that the quadratic polynomial x − 4 is 100-smooth.

This paper constructs an asymptotically complete class of tests (i.e. for a test not within this class one can ...nd a test within the class that has better or equal asymptotical powerfunction) for testing one parametric restriction when the likelihoodfunction can asymptotically be approximated by a quadratic function: The coe¢cients of this quadratic form may be random variables, so that our r...

A new method for determining knots in parametric curve interpolation is presented. The determined knots have a quadratic polynomial precision in the sense that an interpolation scheme which reproduces quadratic polynomials would reproduce parametric quadratic polynomials if the new method is used to determine knots in the interpolation process. Testing results on the efficiency of the new metho...

Three approaches are currently used for devising identitybased encryption schemes. They respectively build on pairings, quadratic residues (QR), and lattices. Among them, the QR-based scheme proposed by Cocks in 2001 is notable in that it works in standard RSA groups: its security relies on the standard quadratic residuosity assumption. But it has also a number of deficiencies, some of them hav...

Article history: Received 3 October 2014 Accepted 17 February 2015 Available online 9 March 2015 Submitted by J.F. Queiro MSC: 90C22 15A39 90C20

The problem of moments has been studied for more than a century. This paper discusses a practical issue related to the problem of moments namely the bounding of a distribution based on a given number of moments. The presented approach is unified in the sense that all measures of interests are provided as a quadratic expression of the same Hankel-matrix. Application examples indicate the importa...

In this paper, we prove that there does not exist a set with more than 98 nonzero polynomials in Z[X], such that the product of any two of them plus a quadratic polynomial n is a square of a polynomial from Z[X] (we exclude the possibility that all elements of such set are constant multiples of a linear polynomial p ∈ Z[X] such that p2|n). Specially, we prove that if such a set contains only po...

We consider quadratic eigenproblems (

We focus on a very specific case of the Uniform Boundedness Conjecture, namely, bounding the number of possible c such that the quadratic polynomial φc(z) = z2 + c has quadratic periodic points of some small period. We show that there are infinitely many rational c with quadratic 4-cycles, with all such c completely understood; and only finitely many rational c with quadratic 5-cycles (we conje...

In this paper we prove a function field version of a theorem by Rudnick and Soundararajan about lower bounds for moments of quadratic Dirichlet L–functions. We establish lower bounds for the moments of quadratic Dirichlet L–functions associated to hyperelliptic curves of genus g over a fixed finite field Fq in the large genus g limit.