A variant of the Nagell–Ljunggren superelliptic equation

N. Saradha ()
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N. Saradha: University of Mumbai

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 15-22

Abstract: Abstract In this note we study the finiteness of solutions of the exponential Diophantine equation $$\begin{aligned} \bigg ( \frac{x^d-1}{x-1}\bigg )^2-\frac{x^d(x^{d-1}-1)}{x-1}=y^m \end{aligned}$$ ( x d - 1 x - 1 ) 2 - x d ( x d - 1 - 1 ) x - 1 = y m in rational integers $$x,y, d\ge 1\ \textrm{and}\ m\ge 2.$$ x , y , d ≥ 1 and m ≥ 2 .

Keywords: Exponential Diophantine equations; Hyperelliptic equations; Superelliptic equations; Primary; 11D61 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-022-00342-6

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