#### Glasnik Matematicki, Vol. 46, No. 2 (2011), 325-331.

### ON A VARIANT OF A DIOPHANTINE EQUATION OF CASSELS

### Alain Togbé and Pingzhi Yuan

Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville IN 46391, USA

*e-mail:* `atogbe@pnc.edu`
School of Mathematics, South China Normal University, Guangzhou 510631, P. R. China

*e-mail:* `mcsypz@mail.sysu.edu.cn`

**Abstract.** Recently, Yuan and Li considered a variant *y*^{2}=px(Ax^{2}-2) of Cassels' equation *y*^{2}=3x(x^{2}+2). They proved that the equation has at most five solutions in positive integers *(x, y)*. In this note, we improve Yuan-Li's result by showing that for any prime *p* and any odd positive integer *A*, the Diophantine equation *y*^{2}=px(Ax^{2}-2) has at most three solutions in positive integers *(x, y)*.

**2000 Mathematics Subject Classification.**
11D25, 11B39.

**Key words and phrases.** Diophantine equations.

**Full text (PDF)** (access from subscribing institutions only)
DOI: 10.3336/gm.46.2.04

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