The equation $(x-d)^5+x^5+(x+d)^5=y^n$ (Q4988887)

scientific article; zbMATH DE number 7349965

Language	Label	Description	Also known as
English	The equation $(x-d)^5+x^5+(x+d)^5=y^n$	scientific article; zbMATH DE number 7349965

Statements

instance of

scholarly article

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title

The equation $(x-d)^5+x^5+(x+d)^5=y^n$ (English)

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20 May 2021

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full work available at URL

https://arxiv.org/abs/2006.10349

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zbMATH Keywords

Frey-Hellegouarch curves

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modularity of elliptic curves

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Schinzel-Tijdeman

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describes a project that uses

three_fourth_powers_code

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Magma

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MaRDI profile type

MaRDI publication profile

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cites work

On perfect powers that are sums of cubes of a five term arithmetic progression

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On perfect powers that are sums of cubes of a three term arithmetic progression

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On perfect powers that are sums of cubes of a seven term arithmetic progression

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Klein forms and the generalized superelliptic equation

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On the Diophantine equation $1^k+2^k+\dotsb+x^k=y^n$

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Superelliptic equations arising from sums of consecutive powers

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Ternary Diophantine Equations via Galois Representations and Modular Forms

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The Magma algebra system. I: The user language

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Lucas sequences whose 12th or 9th term is a square

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On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises

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On some generalizations of the diophantine equation $1^k + 2^k + ... + x^k = y^z$

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Chabauty methods using elliptic curves

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Two-cover descent on hyperelliptic curves

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The Mordell–Weil sieve: proving non-existence of rational points on curves

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Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation

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A diophantine equation

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Addendum to a paper of Harada and Lang

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On the equation $1^k + 2^k + ... + x^k = y^z$

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On a conjecture of Schäffer concerning the equation $1^k + \ldots + x^k = y^n$

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Perfect powers that are sums of squares in a three term arithmetic progression

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Sur l'équation a3+ b3= cp

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On the sum of fourth powers in arithmetic progression

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On powers that are sums of consecutive like powers

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A note on the equation $1^ k+2^ k+\cdots+(x-1)^ k=y^ m$

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On the power values of power sums

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On modular representations of $\text{Gal}(\overline{\mathbb Q}/\mathbb Q)$ arising from modular forms

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The equation $1^p+2^p+3^p+\ldots+n^p=m^q$

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On the equation $y^m = P(x)$

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Ring-theoretic properties of certain Hecke algebras

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On a Diophantine equation

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On the equation $f(1)1^k + f(2)2^k + ... + f(x)x^k + R(x)= by^z$

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On the Diophantine equation $1^k+2^k+\dots +x^k+R(x)=y^2$

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Modular elliptic curves and Fermat's Last Theorem

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On the Diophantine equation (x-1)^k+x^k+(x+1)^k=y^n

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On the Diophantine equation (x − d)4 + x4 + (x + d)4 = yn

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Identifiers

zbMATH Open document ID

1475.11049

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DOI

10.4064/aa200617-11-11

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4988887