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On the Golomb’s conjecture and Lehmer’s numbers

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Tingting W., Xiaonan W.

Open Mathematics

2017

tom 15

nr 1

1003-1009

Let p be an odd prime. For each integer a with 1 ≤ a ≤ p − 1, it is clear that there exists one and only one ā with 1 ≤ ā ≤ p − 1 such that a · ā ≡ 1 mod p. Let N(p) denote the set of all primitive roots a mod p with 1 ≤ a ≤ p − 1 in which a and ā are of opposite parity. The main purpose of this paper is using the analytic method and the estimate for the hybrid exponential sums to study the solvability of the congruence a + b ≡ 1 mod p with a, b ∈ N(p), and give a sharper asymptotic formula for the number of the solutions of the congruence equation.

Ograniczanie wyników

1 Open Mathematics

1 Tingting W.

1 Xiaonan W.

1 2017

Wyniki wyszukiwania

On the Golomb’s conjecture and Lehmer’s numbers