On the Diophantine Equation Mpx

被引：7
|
作者：
Gayo, William S., Jr. [1 ,2 ]
Bacani, Jerico B. [1 ]
机构：
[1] Univ Philippines Baguio, Coll Sci, Dept Math & Comp Sci, Baguio 2600, Benguet, Philippines
[2] Don Mariano Marcos Mem State Univ North La Union, Coll Arts & Sci, Gen Educ Dept, Bacnotan 2515, La Union, Philippines
来源：
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2021年 / 14卷 / 02期
关键词：
Diophantine equation; Exponential Diophantine equation; Mersenne primes;
D O I：
10.29020/nybg.ejpam.v14i2.3948
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study and solve the exponential Diophantine equation of the form M-p(x) + (M-q + 1)(y) = z(2) for Mersenne primes M-p and M-q and non-negative integers x,y, and z. We use elementary methods, such as the factoring method and the modular arithmetic method, to prove our research results. Several illustrations are presented, as well as cases where solutions to the Diophantine equation do not exist.
引用
收藏
页码：396 / 403
页数：8
相关论文
共 50 条
  • [31] On a particular Diophantine equation
    MacHale, Des
    MATHEMATICAL GAZETTE, 2005, 89 (515): : 246 - 247
  • [32] On the Diophantine equation ax
    Viriyapong, Chokchai
    Viriyapong, Nongluk
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2023, 18 (03): : 525 - 527
  • [33] DIOPHANTINE EQUATION IN CALCULUS
    MARSTON, HM
    LARSON, LC
    AMERICAN MATHEMATICAL MONTHLY, 1964, 71 (07): : 795 - &
  • [34] A RADICAL DIOPHANTINE EQUATION
    NEWMAN, M
    JOURNAL OF NUMBER THEORY, 1981, 13 (04) : 495 - 498
  • [35] AN EXPONENTIAL DIOPHANTINE EQUATION
    ALEX, LJ
    AMERICAN MATHEMATICAL MONTHLY, 1985, 92 (01): : 63 - 63
  • [36] On a Diophantine Equation of Stroeker
    Luca, Florian
    Stanica, Pantelimon
    Togbe, Alain
    BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2010, 17 (02) : 201 - 208
  • [37] On the Diophantine Equation ax
    Pakapongpun, Apisit
    Chattae, Bunthita
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2022, 17 (02): : 711 - 716
  • [38] UNIVERSAL DIOPHANTINE EQUATION
    JONES, JP
    JOURNAL OF SYMBOLIC LOGIC, 1982, 47 (03) : 549 - 571
  • [39] On the Diophantine Equation ax
    Dokchan, Rakporn
    Panngam, Nopparat
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2025, 20 (01): : 63 - 66
  • [40] A note on a Diophantine equation
    Sandor, Jozsef
    NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2013, 19 (04) : 1 - 3
12345