On Certain Diophantine Equations Related to Triangular and Tetrahedral Numbers
نویسنده
چکیده
In this paper we give solutions of certain diophantine equations related to triangular and tetrahedral numbers and propose several problems connected with these numbers. The material of this paper was presented in part at the 11th International Workshop for Young Mathematicians NUMBER THEORY, Kraków, 14th20th september 2008.
منابع مشابه
Class Numbers of Quadratic Fields Determined by Solvability of Diophantine Equations
In the literature there has been considerable attention given to the exploration of relationships between certain diophantine equations and class numbers of quadratic fields. In this paper we provide criteria for the insolvability of certain diophantine equations. This result is then used to determine when related real quadratic fields have class number bigger than 1. Moreover, based on criteri...
متن کاملOn the structural properties for the cross product of fuzzy numbers with applications
In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...
متن کاملDiophantine Equations and Class Numbers
The goals of this paper are to provide: (I ) sufficient conditions, based on the solvability of certain diophantine equations, for the non-triviality of the dass numbers of certain real quadratic fields; (2) sufficient conditions for the divisibility of the class numbers of certain imaginary quadratic fields by a given integer; and (3) necessary and sufficient conditions for an algebraic intege...
متن کاملDiophantine Equations Related with Linear Binary Recurrences
In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...
متن کاملProposing a Discharge Coefficient Equation for Triangular Labyrinth Spillways Based on Laboratory Studies
Labyrinth spillways are considered as suitable and economic structures because, firstly, their discharge flow rate, under low hydraulic heads, is high, and secondly, they occupy less space. The flow over these spillways is three-dimensional and is influenced by several parameters. This study endeavors to offer a new equation for the calculation of the discharge flow of triangular labyrinth spil...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008