On the Diophantine inequality |X2-cXY2+Y4| ≤ c+2
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;...
Paper Details
Title
On the Diophantine inequality |X2-cXY2+Y4| ≤ c+2
Published Date
Dec 16, 2013
Journal
Volume
48
Issue
2
Pages
291 - 299
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Notes
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