The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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A NOTE ON THE INTEGRAL POINTS ON SOME HYPERBOLAS

  • Ko, Hansaem (Department of Mathematics, SoongSil University) ;
  • Kim, Yeonok (Department of Mathematics, SoongSil University)
  • Received : 2012.12.05
  • Accepted : 2013.07.18
  • Published : 2013.08.31
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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 $\mathfrak{h}^a:x^2-axy+y^2=1$ and $\mathfrak{h}_k:x^2-axy+y^2=-k$ ($k{\in}\mathbb{Z}_{>0}$). To list all the integral points on that hyperbola, we find the number of elements of ${\Omega}_k$.

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References

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