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

DOI10.1007/BF02401100zbMath0071.03702OpenAlexW2588148989MaRDI QIDQ767305

Juan Jorge Schaeffer

Publication date: 1956

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

Full work available at URL: https://doi.org/10.1007/bf02401100

zbMATH Keywords

exponential Diophantine equations

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items

A note on the equation \(1^ k+2^ k+\cdots+(x-1)^ k=y^ m\) ⋮ On the Diophantine equation \((x+1)^2+(x+2)^2+\ldots+(x+d)^2=y^n\) ⋮ On the Diophantine equation \((x+1)^{k}+(x+2)^{k}+\ldots+(2x)^{k}=y^{n}\) ⋮ 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 ⋮ On the solutions of the Diophantine equation \((x-d)^2 +x^2 +(x+d)^2 =y^n\) for \(d\) a prime power ⋮ Polynomial values of (alternating) power sums ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A computational approach for solving $y^2=1^k+2^k+\dotsb+x^k$ ⋮ On the power values of power sums ⋮ On the equation \(1^{k}+2^{k}+\cdots +x^{k}=y^{n}\) for fixed \(x\) ⋮ Towers of 2-covers of hyperelliptic curves ⋮ 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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Diophantine equation \(ax^3+by^3+cz^3=0\)
• Über die diophantische Gleichung \(x^l+y^l=c z^l\)
• On the Equation a x - b y = 1
• AN APPLICATION OF HIGH-SPEED COMPUTING TO FERMAT'S LAST THEOREM
• The Insolubility of Classes of Diophantine Equations
• On the Diophantine equation $| Ax^n -By^n| = 1$, $n = 5$.
• On Classes of Diophantine Equations of Higher Degrees Which Have No Solutions