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On integers which are the sum of a power of 2 and a polynomial value |
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| Authors: | Florian Luca Carlos Gustavo Moreira Carl Pomerance |
| Affiliation: | 1. Mathematical Institute, UNAM Juriquilla, Juriquilla, 76230, Santiago de Querétaro, Querétaro de Arteaga, México 2. School of Mathematics, University of the Witwatersrand, P.O. Box Wits 2050, Witwatersrand, South Africa 3. IMPA, Estrada Dona Castorina, 110, Rio de Janeiro, Brazil 4. Mathematics Department, Dartmouth College, Hanover, NH, 03755, USA |
| Abstract: | Here, we show that if f (x) ∈ ?[x] has degree at least 2 then the set of integers which are of the form 2 k + f (m) for some integers k ≥ 0 and m is of asymptotic density 0. We also make some conjectures and prove some results about integers not of the form |2 k ± m a (m ? 1)|. |
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