ON INTEGRAL SOLUTIONS OF TERNARY QUADRATIC DIOPHANTINE EQUATION
Journal Title: Bulletin of Pure and Applied Sciences Sec. E - Mathematics and Statistics - Year 2018, Vol 37, Issue 2
Abstract
In this paper, we analyze the ternary quadratic homogeneous Diophantine equation for finding its non – zero integer solutions. The proposed equation represents a homogeneous cone and its distinct integer solutions represent a distinct integer point on it. We obtain four different patterns of integer points on the cone. A few interesting properties of different patterns of solutions are presented with the help of special numbers such as Polygonal number, Pyramidal number, Octahedral number, Pronic number, Stella Octangular number and Oblong number. Finally, the three triples of integers generated from the given solution are exhibited which satisfy the equation of the given cone.
Authors and Affiliations
Ashokan Hari Ganesh
Keywords
Related Articles
- EP ID EP531797
- DOI 10.5958/2320-3226.2018.00051.6
- Views 140
- Downloads 0
A NOTE ON SEMIDERIVATIONS
Recently, Filippis et al. introduced the notion of generalized semiderivation [[5], Definition 1.2] in prime rings. Accordingly, let R be a prime ring and F: R→R be an additive mapping. If there exists a semiderivation d...
TYPES OF DOMINATION IN INTUITIONISTIC FUZZY GRAPH BY STRONG ARC AND EFFECTIVE ARC
In this paper, we introduce the definitions of strong arc, non- strong arc, semi μ- strong arc, semi ρ- strong arc, effective arc, semi μ-effective arc and semi ρ-effective arc of intuitionistic fuzzy graph. Further,...
Joule Heating and Radiation Absorption Effects on MHD Convective and Chemically Reactive Flow past a Porous Plate
The aim of this study is to analyze the effects of Joule heating and radiation absorption on MHD convective and chemically reactive flow past an inclined porous plate in the presence of heat source and thermal diffusion....
INDEPENDENT VERIFICATION OF EULER’S FORMULA IN GRAPH THEORY FOR N IDENTICAL CIRCLES
This paper discusses the famous Euler’s formula in graph theory and its independent verification for the case of n identical circles forming a planar graph. A planar connected graph is generated using n circles, and an i...
RELIABILITY ANALYSIS OF A SYSTEM BY USING SUGENO (TSK) FUZZY MODEL
In the present paper the binary assumption is replaced by a fuzzy state assumption, thereby leading to fuzzy reliability estimates. In reliability estimation failure rate estimation is an important parameter. Available...