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On the diophantine equation X 2 − (1 + a 2)Y 4 = −2a

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Abstract

Let a ⩾ 1 be an integer. In this paper, we will prove the equation in the title has at most three positive integer solutions.

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Authors and Affiliations

  1. School of Mathematics, South China Normal University, Guangzhou, 510631, China

    PingZhi Yuan

  2. School of Mathematics & Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China

    ZhongFeng Zhang

Authors
  1. PingZhi Yuan
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  2. ZhongFeng Zhang
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Correspondence to PingZhi Yuan.

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Yuan, P., Zhang, Z. On the diophantine equation X 2 − (1 + a 2)Y 4 = −2a . Sci. China Math. 53, 2143–2158 (2010). https://doi.org/10.1007/s11425-010-4048-x

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  • DOI: https://doi.org/10.1007/s11425-010-4048-x

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