On the Diophantine equation (pq)x

被引：0
|
作者：
Orosram, Wachirarak [1 ]
Tangjai, Wipawee [2 ]
机构：
[1] Buriram Rajabhat Univ, Fac Sci, Dept Math, Buriram 31000, Thailand
[2] Mahasarakham Univ, Fac Sci, Dept Math, Maha Sarakham 44150, Thailand
来源：
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE | 2023年 / 18卷 / 02期
关键词：
Diophantine equation; non-negative integer solution; Catalan's conjectur;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the Diophantine equation ( pq)(x)+( pq)(2s) n(y) = z(2), where p and q are prime numbers such that pq = 3 (mod 20) and n = 5 (mod 20). We show that a non-negative integer solution of such equation exists only if pq + 1 is a square. The solution is also in the form ( x, y, z) = (1 + 2s, 0, ( pq)(s) root pq + 1).
引用
收藏
页码：143 / 147
页数：5
相关论文
共 50 条
  • [41] On the Diophantine Equation (p
    Orosram, Wachirarak
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2023, 16 (04): : 2208 - 2212
  • [42] On the Diophantine equation ax
    Viriyapong, Chokchai
    Viriyapong, Nongluk
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2024, 19 (02): : 449 - 451
  • [43] On the Diophantine Equation px
    Pakapongpun, Apisit
    Chattae, Bunthita
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2022, 17 (04): : 1535 - 1540
  • [44] On the diophantine equation y2 = Πi≤8(x + ki)
    Srikanth, R.
    Subburam, S.
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2018, 128 (04):
  • [45] On the Diophantine Equation Fnx
    Taclay, Richard J.
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2024, 19 (03): : 721 - 724
  • [46] On the diophantine equation x2+2α5β13γ=yn
    Goins, Edray
    Luca, Florian
    Togbe, Alain
    ALGORITHMIC NUMBER THEORY, 2008, 5011 : 430 - +
  • [47] The diophantine equation x2+52k+1 = yn
    Abu Muriefah, FS
    Arif, SA
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1999, 30 (03): : 229 - 231
  • [48] A mean value theorem for the Diophantine equation axy−x−y=n
    Jingjing Huang
    Acta Mathematica Hungarica, 2012, 134 : 68 - 78
  • [49] On the resolution of the Diophantine equation U n + U m = x q
    Bhoi, P. K.
    Rout, S. S.
    Panda, G. K.
    RAMANUJAN JOURNAL, 2025, 66 (02):
  • [50] ON THE SOLUTIONS OF THE DIOPHANTINE EQUATION X(3)+Y(3)+Z(3)=N
    KOYAMA, K
    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 1995, E78A (03) : 444 - 449
12345