Abstract
For any real constants λ 1, λ 2 ∈ (0, 1], let \(n \geqslant \max \{ [\tfrac{1} {{\lambda _1 }}],[\tfrac{1} {{\lambda _2 }}]\} \), m ⩾ 2 be integers. Suppose integers a ∈ [1, λ 1 n] and b ∈ [1, λ 2 n] satisfy the congruence b ≡ a m (mod n). The main purpose of this paper is to study the mean value of (a − b)2k for any fixed positive integer k and obtain some sharp asymptotic formulae.
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Xu, Z. On the difference between an integer and its m-th power mod n . Sci. China Math. 56, 1597–1606 (2013). https://doi.org/10.1007/s11425-013-4639-4
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DOI: https://doi.org/10.1007/s11425-013-4639-4