On the diophantine equation y2 ? D = 2k |
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Authors: | Nicholas Tzanakis |
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Institution: | 8 Solomou Street, Iraklion, Crete, Greece |
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Abstract: | The equation of the title is studied for 1 ≤ D ≤ 100. It is shown that for such values of D the above equation is really interesting only if D = 17, 41, 73, 89, 97. Then, for these values of D, (i) necessary conditions are given for the solvability of the diophantine equations y2 = 2x4 + D and y2 = 8x4 + D, and (ii) y2 ? D = 2k is solved. |
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