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On the number of solutions of  |
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| Authors: | Pingzhi Yuan |
| Institution: | Department of Mathematics, Zhongshan University, Guangzhou 510275, P.R. China |
| Abstract: | In this paper, using a result of Ljunggren and some results on primitive prime factors of Lucas sequences of the first kind, we prove the following results by an elementary argument: if  and  are positive integers, then the simultaneous Pell equations  possesses at most one solution  in positive integers. |
| Keywords: | Simultaneous Diophantine equations Pell equations Lucas sequences |
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