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A note on the Diophantine equation \((x + a_1)^{r_1} + (x + a_2)^{r_2} + \cdots + (x + a_m)^{r_m} = y^n\)

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Abstract

In this paper, we note a generalization of the result of Zhongfeng Zhang (Publ. Math. Debrecen 91:383–390, 2017).

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References

  1. Shorey, T.N., Tijdeman, R.: Exponential Diophantine Equations. Cambridge University Press, Cambridge (1986)

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  2. Zhang, Z.: On the Diophantine equations \((x-1)^{3} + x^{5} + (x + 1)^3 = y^n\) and \((x-1)^{5} + x^{3} + (x + 1)^5 = y^n\). Publ. Math. Debrecen. 91, 383–390 (2017)

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Acknowledgements

I remember Prof. R. Balasubramanian, Prof. R. Srikanth and Prof. R. Thangadurai with my thanks. I thank the Editor and referee of this paper for their valuable commends. I thank the National Board of Higher Mathematics (NBHM) of Department of Atomic Energy of India for their support in my research.

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Correspondence to Sivanarayanapandian Subburam.

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Subburam, S. A note on the Diophantine equation \((x + a_1)^{r_1} + (x + a_2)^{r_2} + \cdots + (x + a_m)^{r_m} = y^n\). Afr. Mat. 30, 957–958 (2019). https://doi.org/10.1007/s13370-019-00693-0

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  • DOI: https://doi.org/10.1007/s13370-019-00693-0

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