Functiones et Approximatio Commentarii Mathematici

On the diophantine equation $X^2-(p^{2m}+1)Y^6=-p^{2m}$

Bo He, Alain Togbé, and Pingzhi Yuan

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Abstract

Let $p$ be a prime and $m$ a positive integer. In this paper, it is shown that the equation in the title has at most four solutions in positive integers $(X, Y)$.

Article information

Source
Funct. Approx. Comment. Math., Volume 43, Number 1 (2010), 31-44.

Dates
First available in Project Euclid: 28 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.facm/1285679144

Digital Object Identifier
doi:10.7169/facm/1285679144

Mathematical Reviews number (MathSciNet)
MR2683572

Zentralblatt MATH identifier
0882.68064

Subjects
Primary: 11D41: Higher degree equations; Fermat's equation 11B39: Fibonacci and Lucas numbers and polynomials and generalizations

Keywords
algebraic approximations Thue's equations elliptic curves

Citation

He, Bo; Togbé, Alain; Yuan, Pingzhi. On the diophantine equation $X^2-(p^{2m}+1)Y^6=-p^{2m}$. Funct. Approx. Comment. Math. 43 (2010), no. 1, 31--44. doi:10.7169/facm/1285679144. https://projecteuclid.org/euclid.facm/1285679144


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References

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