Analogues to Fermat primes related to Pell's equation

被引：0
|
作者：
Koehler, Guenter [1 ]
机构：
[1] Univ Wurzburg, Inst Math, D-97074 Wurzburg, Germany
来源：
ARCHIV DER MATHEMATIK | 2010年 / 94卷 / 01期
关键词：
Fermat primes; Pell's equation; Modular forms;
D O I：
10.1007/s00013-009-0080-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The coefficients of some weight 3 modular forms give reason to study primes of the form p = 2x(2) - 1 = 2dy(2) + 1. If x(a), y(a) are the positive solutions of Pell's equation x(2) - dy(2) = 1, given by x(a) + y(a)root d = (x(1) + y(1)root d)(a), and if p(a) = 2x(a)(2) - 1 is prime, then a = 2(m) is a power of 2. So there are analogues to the Fermat numbers 2(a) + 1.
引用
收藏
页码：49 / 52
页数：4
相关论文
共 50 条
  • [21] Circle map, Fermat's Little Theorem, primes and pseudoprimes
    Leo, M
    Leo, RA
    Soliani, G
    CHAOS SOLITONS & FRACTALS, 2002, 14 (07) : 981 - 987
  • [22] Simultaneous Fermat-Pell-Mahler equations
    Bugeaud, Yann
    Levesque, Claude
    Waldschmidt, Michel
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2011, 79 (3-4): : 357 - 366
  • [23] Fermat's equation in real quaternions
    Littlewood, DE
    Richardson, AR
    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1931, 32 : 235 - 240
  • [24] On a Diophantine equation related to the difference of two Pell numbers
    Cagman, Abdullah
    Polat, Kadirhan
    CONTRIBUTIONS TO MATHEMATICS, 2021, 3 : 37 - 42
  • [25] Formalization of Pell's Equation in the Mizar System
    Acewicz, Marcin
    Pak, Karol
    PROCEEDINGS OF THE 2017 FEDERATED CONFERENCE ON COMPUTER SCIENCE AND INFORMATION SYSTEMS (FEDCSIS), 2017, : 223 - 226
  • [26] PELL'S EQUATION IN POLYNOMIALS AND ADDITIVE EXTENSIONS
    Schmidt, Harry
    QUARTERLY JOURNAL OF MATHEMATICS, 2017, 68 (04): : 1335 - 1355
  • [27] Solvability by real radicals and Fermat primes
    Jensen, CU
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2004, 47 (02): : 229 - 236
  • [28] On the generating functions of Mersenne and Fermat primes
    Pablo A. Panzone
    Collectanea Mathematica, 2012, 63 : 59 - 69
  • [29] On the generating functions of Mersenne and Fermat primes
    Panzone, Pablo A.
    COLLECTANEA MATHEMATICA, 2012, 63 (01) : 59 - 69
  • [30] PHYSICISTS PROOF OF FERMAT THEOREM OF PRIMES
    GUTFREUND, H
    LITTLE, WA
    AMERICAN JOURNAL OF PHYSICS, 1982, 50 (03) : 219 - 220
12345