On the equation x(x +d₁)...(x + (k − 1)d₁) =y(y +d₂)...(y + (mk − 1)d₂)

Saradha, N. ; Shorey, T. N. (1994) On the equation x(x +d₁)...(x + (k − 1)d₁) =y(y +d₂)...(y + (mk − 1)d₂) Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 104 (1). pp. 1-12. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/104/1/1-12/...

Related URL: http://dx.doi.org/10.1007/BF02830870

Abstract

For given positive integers m ≥ 2,d₁ and d₂, we consider the equation of the title in positive integers x, y and k ≥ 2. We show that the equation implies that k is bounded. For a fixed k, we give conditions under which the equation implies that max(x, y) is bounded.

Item Type:	Article
Source:	Copyright of this article belongs to Indian Academy of Sciences.
Keywords:	Exponential Diophantine Equations; Arithmetic-geometric Mean
ID Code:	67724
Deposited On:	31 Oct 2011 13:25
Last Modified:	18 May 2016 14:42

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On the equation x(x +d1)...(x + (k − 1)d1) =y(y +d2)...(y + (mk − 1)d2)

Abstract

On the equation x(x +d₁)...(x + (k − 1)d₁) =y(y +d₂)...(y + (mk − 1)d₂)