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Note on cubic equations in three variables with an infinity of integer solutions

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Summary

Sufficient conditions are given for the equationz 3 =ax 2 +by 2+c to have an infinity of integer solutions.

Literatur

  1. (1)

    L. J. Mordell,Note on cubic diophantine equations z 2 =f(x, y) with an infinity of integral solutions, « Journal of the London Mathematical Society »,17 (1942), 199–203.

  2. (2)

    Davenport andHasse,Die Nullstellen der Kongruenzzetafunctionen in gewissen zyklischen Fällen, « Journal fur die reine und angewandte Mathematik »,172 (1934), 174.

  3. (3)

    L. J. Mordell,The number of solutions of some congruences in two variables, « Mathematische Zeitschrift »,37 (1933), 195.

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Mordell, L.J. Note on cubic equations in three variables with an infinity of integer solutions. Annali di Matematica 29, 301–305 (1949). https://doi.org/10.1007/BF02413934

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Keywords

  • Integer Solution