Luca, F. ; Shorey, T. N. (2005) Diophantine equations with products of consecutive terms in Lucas sequences Journal of Number Theory, 114 (2). pp. 298-311. ISSN 0022-314X
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Official URL: http://www.sciencedirect.com/science/article/pii/S...
Related URL: http://dx.doi.org/10.1016/j.jnt.2004.08.007
Abstract
In this paper, we show that if (un)n≥1 is a Lucas sequence, then the Diophantine equation un.un+1.....un+k=ym in integers n≥1, k≥1, m≥2 and y with |y|>1 has only finitely many solutions. We also determine all such solutions when (un)n≥1 is the sequence of Fibonacci numbers and when un=(xn-1)/(x-1) for all n≥1 with some integer x>1.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Lucas Sequences; Primitive Divisors; Arithmetic Progressions |
| ID Code: | 67713 |
| Deposited On: | 31 Oct 2011 13:28 |
| Last Modified: | 31 Oct 2011 13:28 |
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