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Some Diophantine equations of the form $x^{2}-py^{2} =z$

Author(s): Walter Feit
Journal: Proc. Amer. Math. Soc. 129 (2001), 623-625.
MSC (2000): Primary 11D09, 11R11
Posted: October 2, 2000
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Abstract: Let $p = a^{2} + (2b)^{2}$ be a prime. It is shown that each of the two Diophantine equations $x^{2}-py^{2} =a$ or has integral solutions.

References:

[G]: C. F. Gauss, Disquisitiones Arithmeticae, English Translation by A. A. Clarke S. J., Yale University Press, New Haven, 1966. MR 33:5545
[L]: A.-M. Legendre, Théorie des nombres, Librairie Scientifique et Technique, A. Blanchard, Paris, 1955.


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