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

DOI10.4064/aa-37-1-233-240zbMath0365.10014OpenAlexW775378208MaRDI QIDQ4141303

Robert Tijdeman, Marc Voorhoeve, Kálmán Győry

Publication date: 1980

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

Full work available at URL: https://eudml.org/doc/205696

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Exponential Diophantine equations (11D61)

Related Items (11)

A note on the equation \(1^ k+2^ k+\cdots+(x-1)^ k=y^ m\) ⋮ On the zeros of shifted Bernoulli polynomials ⋮ On the Diophantine equation \(1^k+2^k+\dots +x^k+R(x)=y^2\) ⋮ On the Diophantine equation (x − d)4 + x4 + (x + d)4 = yn ⋮ Polynomial values of (alternating) power sums ⋮ Unnamed Item ⋮ On the equation \(1^{k}+2^{k}+\cdots +x^{k}=y^{n}\) for fixed \(x\) ⋮ The equation $(x-d)^5+x^5+(x+d)^5=y^n$ ⋮ Polynomial values of surface point counting polynomials ⋮ On a conjecture of Schäffer concerning the equation \(1^k + \ldots + x^k = y^n\) ⋮ Perfect powers in sum of three fifth powers

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