Superelliptic equations arising from sums of consecutive powers

DOI10.4064/aa8305-12-2015zbMath1401.11076arXiv1509.06619OpenAlexW2963792763MaRDI QIDQ2804248

Samir Siksek, Vandita Patel, Michael A. Bennett

Publication date: 28 April 2016

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.06619

zbMATH Keywords

Galois representationmodularityexponential equationlevel loweringFrey-Hellegouarch curvemulti-Frey-Hellegouarch

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Galois representations (11F80) Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

Related Items (13)

On perfect powers that are sums of cubes of a five term arithmetic progression ⋮ On the Diophantine equation \((x+1)^{k}+(x+2)^{k}+\ldots+(2x)^{k}=y^{n}\) ⋮ Fermat’s Last Theorem and modular curves over real quadratic fields ⋮ On perfect powers that are sums of cubes of a seven term arithmetic progression ⋮ 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 ⋮ The equation $(x-d)^5+x^5+(x+d)^5=y^n$ ⋮ On the sum of fourth powers in arithmetic progression ⋮ Perfect powers in sum of three fifth powers

Uses Software

• Magma

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