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- Publisher
- Oxford University Press
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/S0024609305017789
- Publisher site
- See Article on Publisher Site
Abstract
Abstract Let m, g, q ∈ N with q ≥ 2 and (m, q − 1) = 1. For n ∈ N, denote by sn(n) the sum of digits of n in the q-ary digital expansion. Given a polynomial f with integer coefficients, degree d ≥ 1, and such that f(N) ⊂ N, it is shown that there exists C = C(f, m, q) > 0 such that for any g ∈ Z, and all large N, |{0≤n≤N:sq(f(n))≡g(mod m)}|≥CNmin(1,2/dt). In the special case m = q = 2 and f(n) = n2, the value C = 1/20 is admissible. 2000 Mathematics Subject Classification 11B85 (primary), 11N37, 11N69 (secondary). © London Mathematical Society
Journal
Bulletin of the London Mathematical Society – Oxford University Press
Published: Feb 1, 2006