On solutions of the simultaneous Pell equations and x(2) - (a(2)-1) y(2)=1 and y(2)

Irmak, Nurettin2019-08-012019-08-0120160031-53031588-2829https://dx.doi.org/10.1007/s10998-016-0137-0https://hdl.handle.net/11480/3583Let be an integer and p prime number. It is well-known that the solutions of the Pell equation have recurrence relations. For the simultaneous Pell equations x(2) - (a(2) - 1) y(2) = 1 y(2) - pz(2) = 1 assume that and . In this paper, we show that if is an odd integer, then there is no positive solution to the system. Moreover, we find the solutions completely for in the cases when is even integer and m = 1.eninfo:eu-repo/semantics/closedAccessDiophantine equationPell equationRecurrenceOn solutions of the simultaneous Pell equations and x(2) - (a(2)-1) y(2)=1 and y(2) - pz(2)=1Article73113013610.1007/s10998-016-0137-02-s2.0-84964430243Q2WOS:000380694300011Q4