A NOTE ON THE INTEGRAL POINTS ON SOME HYPERBOLAS
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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 h^a : x^2 - axy + y^2 = 1 and h_k : x^2 - axy + y^2 = -k (k∊ Z>0). To list all the integral points on that hyperbola, we find the number of elements of Ω_k.
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 h^a : x^2 - axy + y^2 = 1 and h_k : x^2 - axy + y^2 = -k (k∊ Z>0). To list all the integral points on that hyperbola, we find the number of elements of Ω_k.
참고문헌 (12)
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