Original scientific paper

https://doi.org/10.3336/gm.48.2.05

On the Diophantine inequality |X2-cXY2+Y4| ≤ c+2

Bo He ; Department of Mathematics, ABa Teacher's College, Wenchuan, Sichuan 623000, P. R. China
István Pink ; Institute of Mathematics, P. O. Box 12, H-4010 Debrecen, Hungary
Ákos Pintér ; Institute of Mathematics, MTA-DE Research Group, "Equations, Functions and Curves", Hungarian Academy of Sciences and University of Debrecen, P. O. Box 12, H-4010 Debrecen, Hungary
Alain Togbé orcid.org/0000-0002-5882-936X ; Department of Mathematics, Purdue University North Central, 1401 S. U.S. 421, Westville, IN 46391, USA

Abstract

Generalizing some earlier results, we find all the coprime integer solutions of the Diophantine inequality

|X2-cXY2+Y4| ≤ c+2, (X,Y)=1,

except when c ≡ 2 (mod 4), in which case we bound the number of integer solutions. Our work is based on the results on the Diophantine equation AX4-BY2=C, where A, B are positive integers and C ±{1, 2, 4}.

Keywords

Diophantine equations; quartic equations

Hrčak ID:

112209

URI

https://hrcak.srce.hr/112209

Publication date:

16.12.2013.

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