On the Diophantine equation \((x+1)^2+(x+2)^2+\ldots+(x+d)^2=y^n\)

DOI10.7169/facm/2013.49.1.4zbMath1335.11023OpenAlexW2041730195MaRDI QIDQ372725

Meng Bai, Zhongfeng Zhang

Publication date: 21 October 2013

Published in: Functiones et Approximatio. Commentarii Mathematici (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.facm/1379686434

zbMATH Keywords

Diophantine equationsbinomial Thue equations

Mathematics Subject Classification ID

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

Related Items (12)

On perfect powers that are sums of cubes of a five term arithmetic progression ⋮ On the Diophantine equation \((x+1)^{k}+(x+2)^{k}+\ldots+(2x)^{k}=y^{n}\) ⋮ A note on the Diophantine equation \((x+1)^3 + (x+2)^3 + \cdots + (2x)^3 = y^n\) ⋮ On perfect powers that are sums of cubes of a seven term arithmetic progression ⋮ DIOPHANTINE EQUATIONS OF THE FORM OVER FUNCTION FIELDS ⋮ 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 ⋮ Perfect powers in sum of three fifth powers

Cites Work

• Unnamed Item
• The equation \(1^p+2^p+3^p+\ldots+n^p=m^q\)
• On the power values of power sums
• A computational approach for solving $y^2=1^k+2^k+\dotsb+x^k$
• On the Diophantine equation $1^k+2^k+\dotsb+x^k=y^n$

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