Izvorni znanstveni članak

https://doi.org/10.3336/gm.46.2.04

On a variant of a Diophantine equation of Cassels

Alain Togbe orcid.org/0000-0002-5882-936X ; Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville IN 46391, USA
Pingzhi Yuan ; School of Mathematics, South China Normal University, Guangzhou 510631, P. R. China

Sažetak

Recently, Yuan and Li considered a variant y2=px(Ax2-2) of Cassels' equation y2=3x(x2+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 y2=px(Ax2-2) has at most three solutions in positive integers (x, y).

Ključne riječi

Diophantine equations

Hrčak ID:

74262

URI

https://hrcak.srce.hr/74262

Datum izdavanja:

23.11.2011.

Posjeta: 944 *