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A problem of D. H. Lehmer and its generalization. II. (English) Zbl 0798.11001
For an odd integer \(q>2\) let \(L(q)\) denote the set of integers \(a\) in the interval \([1,q-1]\) that are coprime with \(q\) and for which \(a + \overline a \equiv 1 \text{mod} 2\) holds. Here, \(\overline a\) stands for the solution of the congruence \(ax \equiv 1 \text{mod} q\) with \(1 \leq \overline a \leq q-1\). In [Chin. Sci. Bull. 38, No. 16, 1340-1345 (1993; Zbl 0797.11004)] Z. Zheng derived for \(1 \leq N \leq q-1\) the asymptotic formula \[ \sum^ N_{ {a = 1 \atop a \in L(q)}}1 = {N \over 2} \cdot {\varphi (q) \over q} + O \bigl( q^{1/2} d(q) \log^ 2q \bigr), \] where \(d(q)\) is the divisor function. In the present paper the author also proves this result in the case \(N=q-1\).
Reviewer: J.Hinz (Marburg)

MSC:
11A07 Congruences; primitive roots; residue systems
11N69 Distribution of integers in special residue classes
11A15 Power residues, reciprocity
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References:
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