| Pell伴随数列中的三角数 |
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| 引用本文： | 陈历敏.Pell伴随数列中的三角数[J].数学杂志,2012,32(1):147-151. |
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| 作者姓名： | 陈历敏 |
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| 作者单位： | 湛江师范学院数学系,广东湛江,524048 |
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| 摘 要： | 本文研究了数列A(D)中三角数的存在性问题.利用Pell方程和Petr方程的解的性质,得到了数列A(D)含有三角数的三个必要条件,并证明了当D≤20时,数列A(D)仅当D=2,11,14时含有三角数.推广了Prasad与Rao3]和罗明4]的结果.
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| 关 键 词： | Pell伴随数列 三角数 Pell方程 Petr方程 |
THE TRIANGULAR NUMBERS IN ASSOCIATED PELL SEQUENCES |
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| CHEN Li-min.THE TRIANGULAR NUMBERS IN ASSOCIATED PELL SEQUENCES[J].Journal of Mathematics,2012,32(1):147-151. |
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| Authors: | CHEN Li-min |
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| Institution: | CHEN Li-min(Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,China) |
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| Abstract: | The aim of this paper is to study the existence of the triangular numbers in sequences A(D).By using the properties of Pell equation and Petr equation,Three necessary conditions for A(D) contains triangular numbers are given.Moreover,we proved that,for D ≤ 20,the sequence A(D) contains triangular numbers if and only if D = 2,11 and 14,and generalize the results of Prasad3] and Luo4]. |
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| Keywords: | associated Pell sequence triangular number Pell equation Petr equation |
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