English

About certain prime numbers

Number Theory 2009-07-03 v1
Authors: Diana Savin
View on arXiv ↗ PDF ↗

Abstract

We give a necessary condition for the existence of solutions of the Diophantine equation p=xq+ryq,p=x^{q}+ry^{q}, with pp, qq, rr distinct odd prime natural numbers.

Keywords

diophantine equations prime number theory perfect numbers

Cite

@article{arxiv.0907.0315,
  title  = {About certain prime numbers},
  author = {Diana Savin},
  journal= {arXiv preprint arXiv:0907.0315},
  year   = {2009}
}

Comments

Preliminary version

Related papers

View all related →
Number Theory · Mathematics
On the Diophantine equation $pq=x^2+ny^2$
Ja Kyung Koo, Dong Hwa Shin
2014-04-18
Number Theory · Mathematics
On the Diophantine equation cy^l=(x^p-1)/(x-1)
Mohammad Sadek
2013-02-26
General Mathematics · Mathematics
Primes Solutions Of Linear Diophantine Equations
N. A. Carella
2014-04-04
Number Theory · Mathematics
On the Diophantine equation $dx^2+p^{2a}q^{2b}=4y^p$
Kalyan Chakraborty, Azizul Hoque
2021-11-11
Number Theory · Mathematics
On the exponential Diophantine equation $x^2+p^mq^n=2y^p$
Kalyan Chakraborty, Azizul Hoque
2023-08-25
Number Theory · Mathematics
On the Diophantine equation x^4-q^4=py^5
Diana Savin
2009-07-06
History and Overview · Mathematics
On the Diophantine Equation 1/a + 1/b = (q+1) / pq
Jeremiah W. Johnson
2019-05-09
Number Theory · Mathematics
An exponential diophantine equation related to odd perfect numbers
Tomohiro Yamada
2020-12-29
Number Theory · Mathematics
On $px^2 + q^{2n}= y^p$ and related Diophantine equations
A. Laradji, M. Mignotte, N. Tzanakis
2021-08-27
Number Theory · Mathematics
On the Diophantine equation $x^2+q^{2m}=2y^p$
Szabolcs Tengely
2015-06-26
Number Theory · Mathematics
General Solution of the Diophantine equation involving Mersenne Prime
Arkabrata Ghosh
2023-07-25
Number Theory · Mathematics
On the Solutions of the Diophantine Equation $x^n + y^n = z^n$ In the Finite Fields $\mathbb{Z}_p$
Silvia R. Valdes, Yelena Shvets
2020-01-10
Number Theory · Mathematics
On a conjecture on exponential Diophantine equations
Mihai Cipu, Maurice Mignotte
2015-05-13
Number Theory · Mathematics
On the equation $x^2-Dy^2=n$
Dasheng Wei
2011-02-21
Number Theory · Mathematics
On primitive integer solutions of the Diophantine equation $x^3\pm y^3=a^k\pm b^k$
Maciej Ulas
2025-08-26
Number Theory · Mathematics
Representing Primes as the Form $x^2+ny^2$ in Some Imaginary Quadratic Fields
Chang Lv, Yingpu Deng
2015-01-12
Number Theory · Mathematics
On the solutions of $x^2= By^p+Cz^p$ and $2x^2= By^p+Cz^p$ over totally real fields
Narasimha Kumar, Satyabrat Sahoo
2024-11-18
Number Theory · Mathematics
Product of powers of distinct primes as sums of Fibonacci numbers
Herbert Batte, Florian Luca, Volker Ziegler
2026-02-23
Number Theory · Mathematics
The diophantine equation $(2^{k}-1)(b^{k}-1)=y^{q}$
Chang Liu, Bo He
2026-04-09
Number Theory · Mathematics
On the Diophantine Equation $p^x + p^y = z^{2n}$
Dibyajyoti Deb
2017-09-07
Number Theory · Mathematics
On The Solutions of The Equation (4^n)^x+p^y=z^2
Bilge Peker, Selin Inag Cenberci
2012-02-13
Number Theory · Mathematics
Diophantine equations in the primes
Brian Cook, Ákos Magyar
2015-06-18
Number Theory · Mathematics
On the exponential Diophantine equation ${\displaystyle p\cdot 3^{x}+p^{y}=z^2}$ with $p$ a prime number
A. L. P. Porto, M. Buosi, G. S. Ferreira
2023-08-22
General Mathematics · Mathematics
The Rational Number n/p as a sum of two unit fractions
Konstantine Zelator
2012-03-02
Number Theory · Mathematics
The Nagell-Ljunggren equation via Runge's method
Michael A. Bennett, Aaron Levin
2013-12-17
R2 v1 2026-06-21T13:20:24.649Z