On the Lebesgue-Nagell equation

• Autorzy: Andrzej Dąbrowski
• Języki publikacji: EN

Abstrakty

EN

We completely solve the Diophantine equations $x² + 2^{a}{q}^b = yⁿ$ (for q = 17, 29, 41). We also determine all $C = p₁^{a₁} ⋯ p_k^{a_k}$ and $C = 2^{a₀}p₁^{a₁} ⋯ p_k^{a_k}$, where $p₁,...,p_k$ are fixed primes satisfying certain conditions. The corresponding Diophantine equations x² + C = yⁿ may be studied by the method used by Abu Muriefah et al. (2008) and Luca and Togbé (2009).

Kategorie tematyczne

• 11D61: Exponential equations
• 11D41: Higher degree equations; Fermat's equation
• 11Y50: Computer solution of Diophantine equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 125
• Numer: 2
• Strony: 245-253

Daty

wydano

2011

Twórcy

autor

Andrzej Dąbrowski

• Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

Identyfikatory

DOI

10.4064/cm125-2-9