PERFECT POWERS THAT ARE SUMS OF CONSECUTIVE CUBES

DOI10.1112/S0025579316000231zbMath1437.11046arXiv1603.08901MaRDI QIDQ2970174

Samir Siksek, Vandita Patel, Michael A. Bennett

Publication date: 28 March 2017

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.08901

Mathematics Subject Classification ID

Galois representations (11F80) Cubic and quartic Diophantine equations (11D25) Linear forms in logarithms; Baker's method (11J86) Representation problems (11D85)

Related Items (11)

On perfect powers that are sums of cubes of a five term arithmetic progression ⋮ On the Diophantine equation \((x+1)^{k}+(x+2)^{k}+\ldots+(2x)^{k}=y^{n}\) ⋮ On perfect powers that are sums of cubes of a seven term arithmetic progression ⋮ DIOPHANTINE EQUATIONS OF THE FORM OVER FUNCTION FIELDS ⋮ On the Diophantine equation (x − d)4 + x4 + (x + d)4 = yn ⋮ Perfect powers that are sums of squares of an arithmetic progression ⋮ On the solutions of the Diophantine equation \((x-d)^2 +x^2 +(x+d)^2 =y^n\) for \(d\) a prime power ⋮ On powers that are sums of consecutive like powers ⋮ Unnamed Item ⋮ Perfect powers that are sums of squares in a three term arithmetic progression ⋮ Perfect powers in sum of three fifth powers

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
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• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• On the Diophantine equation (x-1)^k+x^k+(x+1)^k=y^n
• Linear forms in two logarithms and interpolation determinants II
• A diophantine equation
• Majorations Effectives Pour L’ Équation de Fermat Généralisée
• On a Diophantine equation

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