On the equation \(1^{k}+2^{k}+\cdots +x^{k}=y^{n}\) for fixed \(x\)

DOI10.1016/J.JNT.2015.11.008zbMath1402.11052OpenAlexW2514955796MaRDI QIDQ5964528

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Publication date: 29 February 2016

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.11.008

zbMATH Keywords

powerspolynomial-exponential equations and congruencespower sumsSchäffer's conjecture

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

Related Items (2)

On the Diophantine equation \((x+1)^{k}+(x+2)^{k}+\ldots+(2x)^{k}=y^{n}\) ⋮ Unnamed Item

Uses Software

• Magma

Cites Work

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• The equation \(1^p+2^p+3^p+\ldots+n^p=m^q\)
• On the power values of power sums
• A note on the equation \(1^ k+2^ k+\cdots+(x-1)^ k=y^ m\)
• The Magma algebra system. I: The user language
• On a conjecture of Schäffer concerning the equation \(1^k + \ldots + x^k = y^n\)
• Linear forms in two logarithms and interpolation determinants II
• On the equation $1^k + 2^k + ... + x^k = y^z$
• A computational approach for solving $y^2=1^k+2^k+\dotsb+x^k$
• On the Diophantine equation $1^k+2^k+\dotsb+x^k=y^n$
• Primary cyclotomic units and a proof of Catalans conjecture
• Equal values of standard counting polynomials

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