An infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five

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Abstract

We construct a new infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five. Let n be a positive integer that satisfy n ≡ ±3 (mod 500) and n ≢ 0 (mod 3). We prove that 5 divides the class numbers of both Q(√<2-F_n>) and Q(√<5(2-F_n)>), where F_n is the nth Fibonacci number.

Journal

  • Journal of number theory

    Journal of number theory (176), 333-343, 2017-07

    Elsevier Inc.

Codes

  • NII Article ID (NAID)
    120006706219
  • NII NACSIS-CAT ID (NCID)
    AA00703731
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0022-314X
  • Data Source
    IR 
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