Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/on-integers-which-are-the-sum-of-a-power-of-2-and-a-polynomial-value-DS5wUCRvJg
References (14)
-
E. Matveev (1998)
An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbersIzvestiya: Mathematics, 62
-
P. Erdös (1950)
On integers of the form 2 k+ p and some related problemsSumma Brasil. Math., 2
-
H. Helfgott (2012)
Minor arcs for Goldbach's problemarXiv: Number Theory
-
(1950)
On de Polignac’s conjecture, (Dutch) Simon Stevin,27 -
F. Cohen, J. Selfridge (1975)
Not every number is the sum or difference of two prime powersMathematics of Computation, 29
-
F. Luca, V. Huguet (2009)
Some remarks on Sierpinski numbers and related problems, 15
-
J.G. Corput (1950)
On de Polignac’s conjecture(Dutch) Simon Stevin, 27
-
F. Cohen, J.L. Selfridge (1975)
Not every number is the sum or difference of two prime powersCollection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday. Math. Comp., 29
-
F. Luca (2002)
On integers which are not differences of two powersMathematika, 49
-
Bob Hough (2013)
Solution of the minimum modulus problem for covering systemsarXiv: Number Theory
-
V. Sprindžuk (1971)
RATIONAL APPROXIMATIONS TO ALGEBRAIC NUMBERSMathematics of The Ussr-izvestiya, 5
-
M. Bennett, F. Luca, J. Mulholland (2010)
TWISTED EXTENSIONS OF THE CUBIC CASE OF FERMAT’S LAST THEOREM -
(1950)
On integers of the form 2k + p and some related problems -
J. Evertse (1996)
An improvement of the quantitative subspace theoremCompositio Mathematica, 101
- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Sociedade Brasileira de Matemática
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-014-0063-9
- Publisher site
- See Article on Publisher Site
Abstract
Here, we show that if f (x) ∈ ℤ[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)|.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Oct 1, 2014