Abstract
Given an integer \(n>1\), it is a classical Diophantine problem that whether n can be written as a sum of two rational cubes. The study of this problem, considering several special cases of n, has a copious history that can be traced back to the works of Sylvester [14], Satgé [11], Selmer [12] etc., and up to the recent works of Alpöge et al. [1]. In this article, we consider the cube sum problem for cube-free integers n which are coprime to 3 and have exactly two distinct prime factors.
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Acknowledgements
The authors would like to thank Somnath Jha for his encouragement, advice, remarks and several e-mail communications. We are also thankful to the anonymous referee(s) for carefully going through the manuscript and providing valuable suggestions that helped improve the readability of this article. Both the authors were partially supported by MHRD SPARC, Grant Number 445. The second author was partially supported by the MHRD Grant SB20210807PHMHRD008128.
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Communicated by B Sury.
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Majumdar, D., Shingavekar, P. Cube sum problem for integers having exactly two distinct prime factors. Proc Math Sci 133, 43 (2023). https://doi.org/10.1007/s12044-023-00757-z
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DOI: https://doi.org/10.1007/s12044-023-00757-z