Integer solutions of a special Diophantine equation
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Date
2011
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Journal ISSN
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Publisher
Amer Inst Pyhsics
Abstract
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).
Description
Bu çalışma, 19-25 Eylül 2011 tarihleri arasında Halkidiki[Yunanistan]’da düzenlenen International Conference on Numerical Analysis and Applied Mathematics (ICNAAM)’da bildiri olarak sunulmuştur.
Keywords
Mathematics, Diophantine equation, Pell equation, Continued fraction, Recurrence relations
Citation
Karasu, 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.