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Some new sums related to D. H. Lehmer problem

Han Zhang, Wenpeng Zhang (2015)

Czechoslovak Mathematical Journal

About Lehmer’s number, many people have studied its various properties, and obtained a series of interesting results. In this paper, we consider a generalized Lehmer problem: Let p be a prime, and let N ( k ; p ) denote the number of all 1 a i p - 1 such that a 1 a 2 a k 1 mod p and 2 a i + a ¯ i + 1 , i = 1 , ...

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