CATALAN EQUATION XP-YQ=1 AND RELATED CONGRUENCES

被引：6

作者：

AALTONEN, M

INKERI, K

机构：

来源：

MATHEMATICS OF COMPUTATION | 1991年 / 56卷 / 193期

关键词：

D O I：

10.2307/2008547

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate solutions of Catalan's equation x(p) - y(q) = 1 in nonzero integers x, y, p, q. By use of class numbers and congruences p(q) = p (mod q2) we show the impossibility of the equation for a large number of prime exponents p, q. Both theoretical and computer results are included. We also study lower bounds on possible, hitherto unknown, solutions x, y > 2; we especially wish to communicate the bound x, y greater-than-or-equal-to 10(500).

引用

页码：359 / 370

页数：12

共 23 条

[1]

Borevich ZI, 1966, NUMBER THEORY

[2]

Brillhart J., 1971, COMPUTERS NUMBER THE, P213

[3] SOLVING EXPONENTIAL DIOPHANTINE EQUATIONS USING LATTICE BASIS REDUCTION ALGORITHMS [J].