A quinary diophantine inequality by primes with one of the form p = x2 + y2+1

被引：0

作者：

Dimitrov, Stoyan ^{[1
]}

机构：

[1] Tech Univ Sofia, Fac Appl Math & Informat, Blvd St Kliment Ohridski 8, Sofia 1756, Bulgaria

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2024年 / 55卷 / 01期

关键词：

Diophantine inequality; Exponential sum; Bombieri; Vinogradov type result; Primes; EXPONENTIAL-SUMS;

D O I：

10.1007/s13226-022-00354-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we show that, for any fixed 1 < c < 5363/3900, every sufficiently large positive number N and a small constant epsilon > 0, the diophantine inequality vertical bar p(1)C + p(2)C + p(3)C + p(4)C + p(5)C - N vertical bar < epsilon has a solution in prime numbers p(1), p(2), p(3), p(4), p(5), such that p(1) = x(2) + y(2) + 1.

引用

页码：168 / 188

页数：21

共 50 条

[21] The Diophantine equation x2
Nguyen Xuan Tho
ANNALES MATHEMATICAE ET INFORMATICAE, 2021, 54 : 121 - 139
[22] A quinary diophantine inequality by primes with one of the form p=x2+y2+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{p=x^2+y^2+1}$$\end{document}
Stoyan Dimitrov
Indian Journal of Pure and Applied Mathematics, 2024, 55 (1) : 168 - 188
[23] On ternary biquadratic Diophantine equation 11(x2 - y2)
Vidhyalakshmi, S.
Gopalan, M. A.
Thangam, S. A.
Ozer, O.
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2019, 25 (03) : 65 - 71
[24] On the diophantine equation x2 + p2k = yn
Attila Bérczes
István Pink
Archiv der Mathematik, 2008, 91 : 505 - 517
[25] On the diophantine equation x2 + p2k = yn
Berczes, Attila
Pink, Istvan
ARCHIV DER MATHEMATIK, 2008, 91 (06) : 505 - 517
[26] On the Diophantine equation x2 − kxy + y2 + lx = 0
Yongzhong Hu
Maohua Le
Chinese Annals of Mathematics, Series B, 2013, 34 : 715 - 718
[27] On the Diophantine equations x2 - Dy2 = -1 and x2 - Dy2 = 4
Chen, Bingzhou
Luo, Jiagui
AIMS MATHEMATICS, 2019, 4 (04): : 1170 - 1180
[28] Constructing x2 for primes p = ax2 + by2
Sun, Zhi-Hong
ADVANCES IN APPLIED MATHEMATICS, 2012, 48 (01) : 106 - 120
[29] ON THE DIOPHANTINE EQUATION x2 + x+1=yz
Schinzel, A.
COLLOQUIUM MATHEMATICUM, 2015, 141 (02) : 243 - 248
[30] Integers of the form x2 + n y2
Cho, Bumkyu
MONATSHEFTE FUR MATHEMATIK, 2014, 174 (02): : 195 - 204

← 1 2 3 4 5 →