The Set of Automorphisms of Pell Forms and Pell Equations

TEKCAN A., Biberoglu G.

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, no.6, pp.783-800, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Journal Name: SOUTHEAST ASIAN BULLETIN OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.783-800
  • Bursa Uludag University Affiliated: Yes

Abstract

d = k(2) + 4 for some integer k >= 2. In this work, we first determined the set of automorphisms of the Pell form F-delta(x, y) = x(2) - dy(2) of discriminant delta = 4d. Later, we deduced the set of all integer solutions of the Pell equations F-delta(x, y) = +/- 1 and F-delta(x, y) = +/- k(2).