On the integers of the form $p^2+b^2+2^n$ and $b_1^2+b_2^2+2^{n^2}$

Details On the integers of the form $p^2+b^2+2^n$ and $b_1^2+b_2^2+2^{n^2}$ On the integers of the form $p^2+b^2+2^n$ and $b_1^2+b_2^2+2^{n^2}$

2008-12-06

arxiv.org/abs/0812.1259v4

Mathematics

Number Theory

17 pages

Scientific paper

We prove that the sumset {p^2+b^2+2^n: p is prime and b,n\in N} has positive
lower density. We also construct a residue class with odd modulo, which
contains no integer of the form p^2+b^2+2^n. And similar results are
established for the sumset {b_1^2+b_2^2+2^{n^2}: b_1,b_2,n\in N}.

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