ON A CONJECTURE OF MORDELL

被引：4

作者：

Chakraborty, Debopam ^{[1
]}

Saikia, Anupam ^{[2
]}

机构：

[1] BITS Pilani, Dept Math, Hyderabad Campus, Hyderabad, India

[2] Indian Inst Technol, Dept Math, Gauhati, Assam, India

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2019年 / 49卷 / 08期

关键词：

Continued fraction; period; fundamental unit; ARTIN-CHOWLA CONJECTURE;

D O I：

10.1216/RMJ-2019-49-8-2545

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A conjecture of Mordell in [12] states that if p is a prime and p is congruent to 3 modulo 4, then p does not divide y where (x, y) is the fundamental solution to x(2) - py(2) = 1. The conjecture has been verified in [2] for primes not exceeding 10(7). In this article, we show that Mordell's conjecture holds for four conjecturally infinite families of primes.

引用

页码：2545 / 2556

页数：12

共 19 条

[1] THE CLASS-NUMBER OF REAL QUADRATIC NUMBER FIELDS [J].

ANKENY, NC ;

ARTIN, E ;

CHOWLA, S .

ANNALS OF MATHEMATICS, 1952, 56 (03) :479-493

[2]

[Anonymous], 2008, The higher arithmetic

[3]

Beach B.D., 1971, P 25 SUMM M CAN MATH, P609

[4]

Bouniakowsky V., 1857, SC MATH PHYS, V6, P305

[5] PROBLEMS ON PERIODIC SIMPLE CONTINUED FRACTIONS [J].

CHOWLA, P ;

CHOWLA, S .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1972, 69 (12) :3745-3745

[6]

Golubeva E.P., 1993, ANAL TEOR CHISEL TEO, V204, p[167, 11]

[7]

Golubeva E.P., 1993, ANAL TEOR CHISEL TEO, V204, p[167, 11]

[8]

Golubeva E.P., 1991, ZAP NAUCHN SEM LENIN, V196, p530 172

[9]

Golubeva E.P., 1993, ZAP NAUCHN SEM S PET, V204

[10]

Golubeva E.P., 1994, J MATH SCI-U TOKYO, V70, P2059

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