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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the integers of the form $p^2+b^2+2^n$ and $b_1^2+b_2^2+2^{n^2}$
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by Hao Pan and Wei Zhang PDF
Math. Comp. 80 (2011), 1849-1864 Request permission

Abstract:

We prove that the sumset $\{p^2+b^2+2^n: p\text { is prime and } b,n\in \mathbb {N}\}$ has positive lower density. We also construct a residue class with an odd modulus that contains no integer of the form $p^2+b^2+2^n$. Similar results are established for the sumset $\{b_1^2+b_2^2+2^{n^2}: b_1,b_2,n\in \mathbb {N}\}.$
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Additional Information
  • Hao Pan
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
  • Email: haopan79@yahoo.com.cn
  • Wei Zhang
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
  • Email: zhangwei_07@yahoo.com.cn
  • Received by editor(s): May 23, 2009
  • Received by editor(s) in revised form: April 25, 2010
  • Published electronically: February 25, 2011
  • Additional Notes: The first author is supported by the National Natural Science Foundation of China (Grant No. 10771135 and 10901078).
  • © Copyright 2011 American Mathematical Society
  • Journal: Math. Comp. 80 (2011), 1849-1864
  • MSC (2010): Primary 11P32; Secondary 11A07, 11B05, 11B25, 11N36
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02445-2
  • MathSciNet review: 2785483