On the diophantine inequality |X^2-cXY^2+Y^4|<=c+2

He, Bo and Pink, István and Pintér, Ákos and Togbé, Alain (2013) On the diophantine inequality |X^2-cXY^2+Y^4|<=c+2. GLASNIK MATEMATICKI, 48 (2). pp. 291-299. ISSN 0017-095X

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Abstract

Generalizing some earlier results, we find all the cop- rime integer solutions of the Diophantine inequality |X2 - cXY 2 + Y 4| <= c + 2; (X; Y ) = 1; except when c == 2 (mod 4), in which case we bound the num- ber of integer solutions. Our work is based on the results on the Diophantine equation AX4 - BY 2 = C; where A;B are positive integers and C 2 �f1; 2; 4g.

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