期刊名称：International Journal of Innovative Research in Science, Engineering and Technology
印刷版ISSN：2347-6710
电子版ISSN：2319-8753
出版年度：2013
卷号：2
期号：4
页码：920
出版社：S&S Publications
摘要：The non-homogeneous quintic equation with three unknowns represented by the diophantine equation2 2 2 5 x y xy x y 1 (k 3) z n is analyzed for its patterns of non-zero distinct integral solutions and three different methods of integral solutions areillustrated. Various interesting relations between the solutions and special numbers, namely, polygonal numbers,Jacobsthal numbers, Jacobsthal-Lucas number,Pronic numbers, Stella octangular numbers, Octahedral numbers, CenteredPolygonal numbers, Centered Pentagonal Pyramidal numbers, Centered Hexagonal Pyramidal numbers, GeneralizedFibonacci and Lucas sequences, Fourth Dimensional Figurate numbers and Fifth Dimensional Figurate numbers areexhibited.
关键词：Integral solutions; Generalized Fibonacci and Lucas sequences; Quintic non-homogeneous equation with;three unknowns
