Note on Pairs of Consecutive Residues of Polynomials
Canadian mathematical bulletin, Tome 11 (1968) no. 1, pp. 79-83
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Let f(x) be a polynomial of degree d ≥ 3 with integral coefficients, 'say, In a previous paper [6] I deduced, from a deep result of Lang and Weil [2], that there is a constant k1(d), depending only on d, such that for all primes p ≥ k1(d), p ⫮ ad, f(x) has a pair of consecutive residues (mod p), that i s, there exists an integer r(0 ≤r ≤ p-1) with the property that
Williams, Kenneth S. Note on Pairs of Consecutive Residues of Polynomials. Canadian mathematical bulletin, Tome 11 (1968) no. 1, pp. 79-83. doi: 10.4153/CMB-1968-011-4
@article{10_4153_CMB_1968_011_4,
author = {Williams, Kenneth S.},
title = {Note on {Pairs} of {Consecutive} {Residues} of {Polynomials}},
journal = {Canadian mathematical bulletin},
pages = {79--83},
year = {1968},
volume = {11},
number = {1},
doi = {10.4153/CMB-1968-011-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-011-4/}
}
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