THE DIOPHANTINE EQUATIONS 2(n) +/- 3.2(m)

被引：0

作者：

Gueth, K. ^{[1
]}

Szalay, L. ^{[2
,3
]}

机构：

[1] Eotvos Lorand Univ, Karoli G Ter 4, H-9700 Szombathely, Hungary

[2] Univ West Hungary, Fac Forestry, Inst Math, H-9400 Sopron, Hungary

[3] J Selye Univ, Bratislavska Cesta 3322, Komarno, Slovakia

来源：

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE | 2018年 / 87卷 / 02期

关键词：

diophantine equations; polynomial-exponential equations; number of bits in squares;

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 equations, 2(n)+/- 3.2(m) + 9 = x(2), and apart from the plus case with the condition, n < m we solve completely the problem. The method resembles the treatment was used, to solve the equation 2(n) + 2(m) + 1 = x(2). The more general problem 2(n) +/- alpha.2(m) + alpha(2) = x(2), where alpha is an odd prime such that 2 is a non-quadratic residue modulo alpha is also considered.

引用

页码：199 / 204

页数：6

共 7 条

[1] PERFECT POWERS WITH THREE DIGITS [J].

Bennett, Michael A. ;

Bugeaud, Yann .

MATHEMATIKA, 2014, 60 (01) :66-84

[2] Perfect powers with few binary digits and related Diophantine problems, II [J].

Bennett, Michael A. ;

Bugeaud, Yann ;

Mignotte, Maurice .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2012, 153 :525-540

[3]

Berczes A., 2016, J COMB NUMBER THEORY, V8, P145

[4] ON THE GENERALIZED RAMANUJAN-NAGELL EQUATION-I [J].

BEUKERS, F .

ACTA ARITHMETICA, 1981, 38 (04) :389-410

[5] On the Diophantine equation 1+2a + xb = yn [J].

Hajdu, Lajos ;

Pink, Istvan .

JOURNAL OF NUMBER THEORY, 2014, 143 :1-13

[6] The diophantine equation x2=pa±pb+1 [J].

Luca, F .

ACTA ARITHMETICA, 2004, 112 (01) :87-101

[7] The equations 2N ± 2M ± 2L = z2 [J].

Szalay, L .

INDAGATIONES MATHEMATICAE-NEW SERIES, 2002, 13 (01) :131-142

← 1 →