The Diophantine equation  |
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| Authors: | Ming-Guang Leu Guan-Wei Li |
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| Institution: | Department of Mathematics, National Central University, Chung-Li, Taiwan 32054, Republic of China ; Department of Mathematics, National Central University, Chung-Li, Taiwan 32054, Republic of China |
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| Abstract: | Let  be a rational prime and  a positive rational integer coprime with  . Denote by  the number of solutions  of the equation  in rational integers  and  . In a paper of Le, he claimed that  without giving a proof. Furthermore, the statement  has been used by Le, Bugeaud and Shorey in their papers to derive results on certain Diophantine equations. In this paper we point out that the statement  is incorrect by proving that  . |
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