Complete solution of a family of simultaneous Pellian equations

@inproceedings{Dujella2004CompleteSO,
  title={Complete solution of a family of simultaneous Pellian equations},
  author={Andrej Dujella},
  year={2004}
}
Let ck = P 2 2k + 1, where Pk denotes the k th Pell number. It is proved that for all positive integers k all solutions of the system of simultaneous Pellian equations z − ckx = ck − 1, 2z − cky = ck − 2 are given by (x, y, z) = (0,±1,±P2k). This result implies that there does not exist positive integers d > c > 2 such that the product of any two distinct elements of the set {1, 2, c, d} diminished by 1 is a perfect square. 1991 Mathematics Subject Classification: 11D09, 11D25 

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