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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 
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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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