Hayder R. Hashim - Solutions of the Diophantine Equation7X2 + Y7 = Z2from Recurrence Sequences

cm:9500 - Communications in Mathematics, July 9, 2020, Volume 28 (2020), Issue 1 - https://doi.org/10.2478/cm-2020-0005
Solutions of the Diophantine Equation7X2 + Y7 = Z2from Recurrence SequencesArticle

Authors: Hayder R. Hashim ORCID

    Consider the system x 2 − ay 2 = b, P (x, y) = z 2, where P is a given integer polynomial. Historically, the integer solutions of such systems have been investigated by many authors using the congruence arguments and the quadratic reciprocity. In this paper, we use Kedlaya’s procedure and the techniques of using congruence arguments with the quadratic reciprocity to investigate the solutions of the Diophantine equation 7X 2 + Y 7 = Z 2 if (X, Y) = (L n , F n ) (or (X, Y) = (F n , L n )) where {F n } and {L n } represent the sequences of Fibonacci numbers and Lucas numbers respectively.


    Volume: Volume 28 (2020), Issue 1
    Published on: July 9, 2020
    Imported on: May 11, 2022
    Keywords: [MATH]Mathematics [math]

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