Simos, T. E.2022-10-062022-10-062011Karasu, A. vd. (2011). "Integer solutions of a special Diophantine equation". ed. T. E. Simos. AIP Conference Proceedings, Numerical Analysis and Applied Mathematics Icnaam 2011: International Conference on Numerical Analysis and Applied Mathematics, 1389, 371-374.0094-243Xhttps://doi.org/10.1063/1.3637759https://aip.scitation.org/doi/abs/10.1063/1.3637759?journalCode=apchttp://hdl.handle.net/11452/28985Bu çalışma, 19-25 Eylül 2011 tarihleri arasında Halkidiki[Yunanistan]’da düzenlenen International Conference on Numerical Analysis and Applied Mathematics (ICNAAM)’da bildiri olarak sunulmuştur.Let t not equal 1 be an integer. In this work, we determine the integer solutions of Diophantine equation D : x(2) + (2-t(2))y(2)+(-2t(2) - 2t + 2)x+(2t(5) - 6t(3) + 4t)y - t(8) + 4t(6) - 4t(4) + 2t(3) + t(2) - 2t - 0 over Z and also over finite fields F-p for primes p >= 2. Also we derive some recurrence relations on the integer solutions (x(n), y(n)) of D and formulate the the n-th solution (x(n), y(n)) by using the simple continued fraction expansion of x(n)/y(n).eninfo:eu-repo/semantics/closedAccessMathematicsDiophantine equationPell equationContinued fractionRecurrence relationsProceedings Paper0003022398000912-s2.0-818552032883713741389Mathematics, appliedReal Quadratic Fields; Pell's Equation; Number Field