바로가기메뉴

본문 바로가기 주메뉴 바로가기

ACOMS+ 및 학술지 리포지터리 설명회

  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
  • 2024년 07월 03일(수) 13:30
사전등록 바로가기
 

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

논문 상세

다음
논문 투고

Vol.20 No.3

Citation Share

A NOTE ON THE INTEGRAL POINTS ON SOME HYPERBOLAS

A NOTE ON THE INTEGRAL POINTS ON SOME HYPERBOLAS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.3, pp.137-148
https://doi.org/10.7468/jksmeb.2013.20.3.137
Ko, Hansaem (Department of Mathematics, SoongSil University)
Kim, Yeonok (Department of Mathematics, SoongSil University)
Ko, Hansaem, & Kim, Yeonok. (2013). A NOTE ON THE INTEGRAL POINTS ON SOME HYPERBOLAS. 한국수학교육학회지시리즈B:순수및응용수학, 20(3), 137-148, https://doi.org/10.7468/jksmeb.2013.20.3.137

Abstract

In this paper, we study the Lie-generalized Fibonacci sequence and the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We derive several interesting properties of the Lie-Fibonacci sequence and relationship between them. We also give a couple of sufficient conditions for the existence of the integral points on the hyperbola <TEX>$\mathfrak{h}^a:x^2-axy+y^2=1$</TEX> and <TEX>$\mathfrak{h}_k:x^2-axy+y^2=-k$</TEX> (<TEX>$k{\in}\mathbb{Z}_{</TEX><TEX>></TEX><TEX>0}$</TEX>). To list all the integral points on that hyperbola, we find the number of elements of <TEX>${\Omega}_k$</TEX>.

keywords
Lie-Fibonacci sequence, Lie-Fibonacci number, Kac-Moody algebra, hyperbolic type

참고문헌

1.

The golden ratio and Fibonacci numbers.

2.

(1980). A hyperbolic GCM and the Fibonacci numbers. Proc. Amer. Math. Soc., 80, 379-385. 10.1090/S0002-9939-1980-0580988-6.

3.

(1961). A Generalized the Fibonacci Sequence. Proc. Amer. Math. Monthly, 68, 455-459. 10.2307/2311099.

4.

Infinite-Dimensional Lie Algebras.

5.

(1995). Rank 2 Symmetric Hyperbolic Kac-Moody Algebras. Nagoya. Math. J., 140, 41-75.

6.

(2004). On the degree of nilpotency of certain subalgebras of Kac-Moody Lie algebras. J. Lie Theory, 14, 11-23.

7.

(2010). A note on the rank 2 symmetric Hyperbolic Kac-Moody Lie algebras. J. KSME. SerB, 17, 107-113.

8.

On some behavior of integral points on a hyperbola.

9.

(1979). Root System of Hyperbolic Type. Adv. in Math., 33, 144-160. 10.1016/S0001-8708(79)80003-1.

10.

(1980). Some remark on an identy of Catalan concerning the Fibonachi numbers. Portugale Math. Soc., 39, 341-348.

11.

(1953). Some Properties of Fibonacci numbers. Amer. Math. Monthly, 60, 680-684. 10.2307/2307147.

12.

(1968). A new class of Lie algebras. J. Algebra, 10, 210-230.

한국수학교육학회지시리즈B:순수및응용수학

논문 투고 OA 정책