ON THE DIOPHANTINE EQUATION ax(3)

被引：1
|
作者：
Subburam, Sivanarayanapandian [1 ]
Thangadurai, Ravindrananathan [2 ]
机构：
[1] Inst Math Sci, CIT Campus, Chennai 600113, Tamil Nadu, India
[2] Harish Chandra Res Inst, Allahabad 211019, Uttar Pradesh, India
来源：
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI | 2015年 / 53卷 / 01期
关键词：
Diophantine equations; positive solutions; upper bound for solutions; divisors in residue classes;
D O I：
10.7169/facm/2015.53.1.9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Consider the diophantine equation ax(3) + by + c = xyz, where a, b and c are positive integers such that gcd (a, c) = 1 and c is square-free. Let (x, y, z) be a positive integral solution of the equation. In this paper, we shall give an upper bound for x, y and z in terms of the given inputs a, b and c. Also, we apply our results to investigate the divisors of the elements of the sequence {an(3) + c} in residue classes.
引用
收藏
页码：167 / 175
页数：9
相关论文
共 50 条
  • [21] On the Diophantine equation Ln = (x 5)
    Tengely, Szabolcs
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2011, 79 (3-4): : 749 - 758
  • [22] An Exponential Diophantine Equation x2
    Muthuvel, S.
    Venkatraman, R.
    INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2024, 19 (04) : 1125 - 1128
  • [23] ON THE DIOPHANTINE EQUATION h(a)x2
    Berbara, Nacira
    Kihel, Omar
    Mavecha, Sukrawan
    Midgley, Joel
    FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2019, 61 (02) : 201 - 206
  • [24] On the exponential diophantine equation xy + yx = zz
    Xiaoying Du
    Czechoslovak Mathematical Journal, 2017, 67 : 645 - 653
  • [25] The Diophantine equation f(x)=g(y)
    Bilu, YF
    Tichy, RF
    ACTA ARITHMETICA, 2000, 95 (03) : 261 - 288
  • [26] On the Diophantine equation σ2(Xn) = σn(Xn)
    Miska, Piotr
    Ulas, Maciej
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2024, 20 (05) : 1287 - 1306
  • [27] ON THE DIOPHANTINE EQUATION 2(x) = x(2)
    Gica, Alexandru
    Luca, Florian
    FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2012, 46 (01) : 109 - 116
  • [28] On the Diophantine equation F(x) = G(y)
    Tengely, S
    ACTA ARITHMETICA, 2003, 110 (02) : 185 - 200
  • [29] On the Positive Integral Solutions of the Diophantine Equation x3 + by+1-xyz=0
    Luca, Florian
    Togbe, Alain
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2008, 31 (02) : 129 - 134
  • [30] On the diophantine equation Gn(x) = Gm(P(x))
    Fuchs, C
    Petho, A
    Tichy, RF
    MONATSHEFTE FUR MATHEMATIK, 2002, 137 (03): : 173 - 196
12345