×

On the Diophantine equation \(1^k+2^k+\dots +x^k+R(x)=y^2\). (English) Zbl 0426.10019


MSC:

11D61 Exponential Diophantine equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Györy, K., Tijdeman, R. & Voorhoeve, M., On the equation 1 k +2 k +...+x k =y z .Acta Arith., 37 to appear. · Zbl 0365.10014
[2] Le Veque, W. J., On the equationy m =f(x).Acta Arith., 9 (1964), 209–219.
[3] Rademacher, H.,Topics in Analytic Number Theory. Springer Verlag, Berlin, 1973. · Zbl 0253.10002
[4] Schäffer, J. J., The equation 1 p +2 p +3 p +...+n p =m q .Acta Math., 95 (1956), 155–159. · Zbl 0071.03702 · doi:10.1007/BF02401100
[5] Schinzel, A. &Tijdeman, R., On the equationy m =P(x) Acta Arith., 31 (1976), 199–204. · Zbl 0303.10016
[6] Shorey, T. N., van der Poorten, A. J., Tijdeman, R. & Schinzel, A., Applications of the Gel’fond-Baker method to Diophantine equations.Transcendence Theory: Advances and Applications, pp. 59–78, Academic Press, 1977. · Zbl 0371.10015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.