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Cubic Diophantine equations: the necessary congruence condition

Published online by Cambridge University Press:  26 February 2010

G. L. Watson
G. L. Watson
Affiliation:
University College, London
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Extract

1. Let p be a prime, t a positive integer, and ϕ a cubic polynomial with integral coefficients, and an integral constant term. We study the congruence

because of its obvious connection with the equation

Type
Research Article
Information
Mathematika , Volume 12 , Issue 1 , June 1965 , pp. 30 - 38
Copyright
Copyright © University College London 1965

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References

1. Davenport, H. and Lewis, D. J., “Non-homogeneous cubic equations”, Journal London Math. Soc., 39 (1964), 657–672.CrossRefGoogle Scholar
2. Watson, G. L., “Quadratic Diophantine equations”, Phil. Trans. Royal Soc, (A) 253 (1960), 227–254.Google Scholar
3. Watson, G. L., Integral quadratic forms (Cambridge, 1960).Google Scholar
4. Watson, G. L.. “Cubic congruences”, Mathematika, 11 (1964), 142–150.CrossRefGoogle Scholar