Geodesic
Representation of integers as sums of fractional powers of primes and powers of 2
Wenbin Zhu1
1School of Mathematics Shandong University 27 Shanda Nanlu Jinan, Shandong 250100, P.R. China
Acta Arithmetica, Tome 181 (2017) no. 2, pp. 185-196

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DOI

Let $c$ be a real number with $1 \lt c \lt 2$. We consider the representation of integers in the form $$N=[p_1^c]+[p_2^c]+2^{\nu_1}+\cdots+2^{\nu_k},$$ where $p$ and $\nu$ denote a prime number and a positive integer respectively. We prove that when $1 \lt c \lt 29/28$, there exists an integer $k$ depending on $c$ such that each large integer $N$ can be represented in the form above.
DOI : 10.4064/aa8663-5-2017
Keywords: real number consider representation integers form cdots where denote prime number positive integer respectively prove there exists integer depending each large integer represented form above

Wenbin Zhu  1

1 School of Mathematics Shandong University 27 Shanda Nanlu Jinan, Shandong 250100, P.R. China 
Wenbin Zhu. Representation of integers as sums of fractional powers of primes and powers of 2. Acta Arithmetica, Tome 181 (2017) no. 2, pp. 185-196. doi: 10.4064/aa8663-5-2017
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