A diophantine equation involving special prime numbers

Stoyan Dimitrov

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 1, page 151-176
  • ISSN: 0011-4642

Abstract

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Let [ · ] be the floor function. In this paper, we prove by asymptotic formula that when 1 < c < 3441 2539 , then every sufficiently large positive integer N can be represented in the form N = [ p 1 c ] + [ p 2 c ] + [ p 3 c ] + [ p 4 c ] + [ p 5 c ] , where p 1 , p 2 , p 3 , p 4 , p 5 are primes such that p 1 = x 2 + y 2 + 1 .

How to cite

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Dimitrov, Stoyan. "A diophantine equation involving special prime numbers." Czechoslovak Mathematical Journal 73.1 (2023): 151-176. <http://eudml.org/doc/299581>.

@article{Dimitrov2023,
abstract = {Let $[\{\cdot \}]$ be the floor function. In this paper, we prove by asymptotic formula that when $1<c<\frac\{3441\}\{2539\}$, then every sufficiently large positive integer $N$ can be represented in the form \[ N=[p^c\_1]+[p^c\_2]+[p^c\_3]+[p^c\_4]+[p^c\_5], \] where $p_1$, $p_2$, $p_3$, $p_4$, $p_5$ are primes such that $p_1=x^2 + y^2 +1$.},
author = {Dimitrov, Stoyan},
journal = {Czechoslovak Mathematical Journal},
keywords = {Diophantine equation; prime; exponential sum; asymptotic formula},
language = {eng},
number = {1},
pages = {151-176},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A diophantine equation involving special prime numbers},
url = {http://eudml.org/doc/299581},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Dimitrov, Stoyan
TI - A diophantine equation involving special prime numbers
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 1
SP - 151
EP - 176
AB - Let $[{\cdot }]$ be the floor function. In this paper, we prove by asymptotic formula that when $1<c<\frac{3441}{2539}$, then every sufficiently large positive integer $N$ can be represented in the form \[ N=[p^c_1]+[p^c_2]+[p^c_3]+[p^c_4]+[p^c_5], \] where $p_1$, $p_2$, $p_3$, $p_4$, $p_5$ are primes such that $p_1=x^2 + y^2 +1$.
LA - eng
KW - Diophantine equation; prime; exponential sum; asymptotic formula
UR - http://eudml.org/doc/299581
ER -

References

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