On Symmetric Square Values of Quadratic Polynomials
نویسنده
چکیده
We prove that there does not exist a non-square quadratic polynomial with integer coefficients and an axis of symmetry which takes square values for N consecutive integers for N = 7 or N ≥ 9. At the opposite, if N ≤ 6 or N = 8 there are infinitely many.
منابع مشابه
Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials
Let K be a field, f = ( f1, . . . , fm) and g = (g1, . . . ,gm) be two sets of m > 1 non-linear polynomials over K[x1, . . . ,xn]. We consider the computational problem of finding – if any – an invertible transformation on the variables mapping f to g. The corresponding equivalence problem is known as Isomorphism of Polynomials with one Secret (IP1S) and is a fundamental problem in multivariate...
متن کاملPolynomial-time algorithms for quadratic isomorphism of polynomials: The regular case
Let f = (f1, . . . , fm) and g = (g1, . . . , gm) be two sets of m ≥ 1 nonlinear polynomials over K[x1, . . . , xn] (K being a field). We consider the computational problem of finding – if any – an invertible transformation on the variables mapping f to g. The corresponding equivalence problem is known as Isomorphism of Polynomials with one Secret (IP1S) and is a fundamental problem in multivar...
متن کاملBuckling and vibration analysis of angle -ply symmetric laminated composite plates with fully elastic boundaries
The main focus of this paper is on efficiency analysis of two kinds of approximating functions (characteristic orthogonal polynomials and characteristic beam functions) that have been applied in the Rayleigh-Ritz method to determine the non-dimensional buckling and frequency parameters of an angle ply symmetric laminated composite plate with fully elastic boundaries. It has been observed that o...
متن کاملGlobal convergence of an inexact interior-point method for convex quadratic symmetric cone programming
In this paper, we propose a feasible interior-point method for convex quadratic programming over symmetric cones. The proposed algorithm relaxes the accuracy requirements in the solution of the Newton equation system, by using an inexact Newton direction. Furthermore, we obtain an acceptable level of error in the inexact algorithm on convex quadratic symmetric cone programmin...
متن کاملBounds on the Pythagoras number of the sum of square magnitudes of complex polynomials
This paper presents lower and upper bounds on the Pythagoras number of sum of square magnitudes of complex polynomials using well-known results on a system of quadratic polynomial equations. Applying this method, a new proof for the upper bound of the Pythagoras number of real polynomials is also presented.
متن کامل