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Minimal Solutions of Diophantine Equations

Published online by Cambridge University Press:  20 November 2018

L. Holzer
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Our aim is to prove: If a, b, c are positive integers, if ab > 1, if a, b, c are relatively prime in pairs, and all are free of squares, if — ab is a quadratic residue of c, bc of a, ca of b, and if F(x, y, z) = ax2 + by2 — cz2, we have non-trivial solutions of

with the inequalities

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Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 238 - 244
Copyright
Copyright © Canadian Mathematical Society 1950