A Computational Approach For
نویسنده
چکیده
We present a computational approach for finding all integral solutions of the equation y2 = 1k + 2k + · · ·+xk for even values of k. By reducing this problem to that of finding integral solutions of a certain class of quartic equations closely related to the Pell equations, we are able to apply the powerful computational machinery related to quadratic number fields. Using our approach, we determine all integral solutions for 2 ≤ k ≤ 70 assuming the Generalized Riemann Hypothesis, and for 2 ≤ k ≤ 58 unconditionally.
منابع مشابه
Stability Assessment Metamorphic Approach (SAMA) for Effective Scheduling based on Fault Tolerance in Computational Grid
Grid Computing allows coordinated and controlled resource sharing and problem solving in multi-institutional, dynamic virtual organizations. Moreover, fault tolerance and task scheduling is an important issue for large scale computational grid because of its unreliable nature of grid resources. Commonly exploited techniques to realize fault tolerance is periodic Checkpointing that periodically ...
متن کاملA dynamic programming approach for solving nonlinear knapsack problems
Nonlinear Knapsack Problems (NKP) are the alternative formulation for the multiple-choice knapsack problems. A powerful approach for solving NKP is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. Despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...
متن کاملA Computational Approach to the Flow of Walter’s Liquid B′ through Annulus of Coaxial Porous Circular Cylinders for High Suction Parameter (RESEARCH NOTE)
The present investigation studies the behavior of steady flow of visco-elastic liquid between two porous coaxial circular cylinders, where both the cylinders are rotating with different uniform angular velocities about the common axis. In addition, the inner cylinder has uniform velocity along the axis and the visco-elastic fluid, which is a Walters liquid B′, is allowed to flow in the annulus....
متن کاملComputational plays in applicable ethics with an Islamic approach
Childhood and adolescence may be regarded to be the most sensitive periods with regard to education and playing is an essential need for children and adolescents. Today computational plays are the main rivals in their plays and take more than forty millions hours of our children and adolescent`s time daily. The researches performed on the destructive and useful effects of computational plays ha...
متن کاملA New Stress Based Approach for Nonlinear Finite Element Analysis
This article demonstrates a new approach for nonlinear finite element analysis. The methodology is very suitable and gives very accurate results in linear as well as in nonlinear range of the material behavior. Proposed methodology can be regarded as stress based finite element analysis as it is required to define the stress distribution within the structural body with structural idealization a...
متن کاملComputational fluid dynamics study and GA modeling approach of the bend angle effect on thermal-hydraulic characteristics in zigzag channels
In the study, the thermal-hydraulic performance of the zigzag channels with circular cross-section was analyzed by Computational Fluid Dynamics (CFD). The standard K-Ꜫ turbulent scalable wall functions were used for modeling. The wall temperature was assumed constant 353 K and water was used as the working fluid. The zigzag serpentine channels with bend angles of 5 - 45° were studied for turbul...
متن کامل