Almost fifth powers in arithmetic progression

DOI10.1016/j.jnt.2011.04.009zbMath1253.11045OpenAlexW1976425371MaRDI QIDQ555292

Lajos Hajdu, Tünde Kovács

Publication date: 22 July 2011

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2011.04.009

zbMATH Keywords

arithmetic progressionperfect powersgenus 2 curvesChabauty method

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Arithmetic progressions (11B25)

Related Items (2)

Powers from products of terms in progressions with gaps ⋮ The Diophantine equation f(x)=g(y)$f(x)=g(y)$ for polynomials with simple rational roots

Uses Software

• Magma

Cites Work

• The product of consecutive integers is never a power
• The Magma algebra system. I: The user language
• Modular elliptic curves and Fermat's Last Theorem
• On the equation $a^p + 2^α b^p + c^p = 0$
• POWERS FROM PRODUCTS OF CONSECUTIVE TERMS IN ARITHMETIC PROGRESSION
• Perfect powers from products of consecutive terms in arithmetic progression
• Some ternary Diophantine equations of signature (n, n, 2)
• Note on the paper ``An extension of a theorem of Euler" by Hirata-Kohno et al. (Acta Arith. 129 (2007), 71–102)
• On perfect powers in products with terms from arithmetic progressions
• On the diophantine equation $n(n+1)...(n+k-1) = bx^l$
• Majorations Effectives Pour L’ Équation de Fermat Généralisée
• Chabauty methods using elliptic curves
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• Ternary Diophantine equations of signature (p, p, 3)
• On the Diophantine Equation n(n + d) · · · (n + (k − 1)d) = by^l
• An extension of a theorem of Euler
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