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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