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Pairs of Consecutive Residues of Polynomials

Published online by Cambridge University Press:  20 November 2018

Kenneth S. Williams
Kenneth S. Williams*
Affiliation:
University of Manchester, Manchester 13, England
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Let p be a large prime and let ƒ(x) be a polynomial of fixed degree d ⩾ 4 with integral coefficients, say,

1.1

Recently Mordell (8) has considered the problem of estimating the least positive residue of ƒ(x) (mod p), that is, the unique integer l (0 ⩽ l ⩽ p — 1) such that the congruence

1.2

is soluble for r = l but not for r = 0, 1, … , l — 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 655 - 666
Copyright
Copyright © Canadian Mathematical Society 1967

References

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