On the Number of Rational Squares at Fixed Distance from a Fifth Power
نویسنده
چکیده
The main result of this note is that there are at most seven rational points (including the one at infinity) on the curve CA with the affine equation y = x+A (where A is a tenth power free integer) when the Mordell-Weil rank of the Jacobian of CA is one. This bound is attained for A = 18 .
منابع مشابه
Optimization of RFM's Structure Using a New Reformulation of PSO in Case of Limited GCPs
Metaheuristic algorithms have been widely used in determining the optimum rational polynomial coefficients (RPCs). By eliminating a number of unnecessary RPCs, these algorithms increase the accuracy of geometric correction of high-resolution satellite images. To this end, these algorithms use ordinary least squares and a number of ground control points (GCPs) to determine RPCs' values. Due to t...
متن کاملEstimation of Hydrodynamic Force on Rough Circular Cylinders in Random Waves and Currents (RESEARCH NOTE)
Most of the Codes of Practice (API, BSI, DnV, NPD) uses Morison's equation to estimate hydrodynamic loads on fixed and moving offshore structures. The significant difference in the prediction of the loads mainly arises from the assumption of the values of hydrodynamic coefficients. In this paper by analysing a full scale set of data in large KC's numbers collected from Delta Wave Flume in the N...
متن کاملOn the fixed number of graphs
A set of vertices $S$ of a graph $G$ is called a fixing set of $G$, if only the trivial automorphism of $G$ fixes every vertex in $S$. The fixing number of a graph is the smallest cardinality of a fixing set. The fixed number of a graph $G$ is the minimum $k$, such that every $k$-set of vertices of $G$ is a fixing set of $G$. A graph $G$ is called a $k$-fixed graph, if its fix...
متن کاملطراحی بهینه مقسم توان 6 دهانه ای با نسبت توان خروجی اختیاری
An effective design procedure is devised for the optimum design of a versatile and useful six-port planar microstrip power divider. An equivalent circuit is developed for the divider; which is composed of line sections and asymmetrical T-junctions. The method of least squares is applied to the equivalent circuit of the divider for its optimum design. This power divider is capable of providing v...
متن کامل