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Note on Pairs of Consecutive Residues of Polynomials
Published online by Cambridge University Press: 20 November 2018
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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
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