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Cubic polynomials with the same residues (mod p)

Published online by Cambridge University Press:  24 October 2008

K. McCann  and
K. S. Williams
K. McCann
Affiliation:
University of Manchester
K. S. Williams
Affiliation:
University of Manchester
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Extract

Some recent work by the authors (1) on the distribution of the residues of a cubic polynomial modulo an odd prime p led to the conjecture that, in general, two cubic polynomials with integer coefficients possessing the same residues modulo p (not necessarily occurring to the same multiplicity) are equivalent, that is are related by a linear transformation modulo p. The purpose of the present paper is to prove this conjecture. We establish the following theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 655 - 658
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)McCann, K. and Williams, K. S.On the residues of a cubic polynomial (mod p) Canad. Math. Bull., 10 (1967), 29–38.Google Scholar
(2)Perel'muter, G. I.On certain sums of characters, Uspehi Mat. Nauk., (2), 18 (1963), 145–9.Google Scholar