О дискриминанте квадратичного поля с промежуточными дробями отрицательной нормы и разложимости его представляющего многочлена

Translated title of the contribution: On the discriminant of a quadratic field with intermediate fractions of negative norm and the decomposability of its representing polynomial

Research output: Contribution to journalArticlepeer-review

Abstract

The work is devoted to the study of Diophantine equation x2 — y2(p2 — 4q) = 4t, where p = l + u(k2 — 1)(l(k2 — 1) — 2k) q = u(lk3 — 2k2 — kl + 1) + km + 1, l = k + m(k2 — 1) numbers k,m,u are nonnegative integers, number k is odd, and the right hand side 4t of the equation is sufficiently small positive integer. We give a complete description of solutions of the Diophantine equation.

Translated title of the contributionOn the discriminant of a quadratic field with intermediate fractions of negative norm and the decomposability of its representing polynomial
Original languageRussian
Article number21
Pages (from-to)319-331
Number of pages13
JournalSiberian Electronic Mathematical Reports
Volume18
DOIs
Publication statusPublished - 2021

Keywords

  • diophantine approximations
  • diophantine equation
  • generalized Pell’s equation
  • integer solutions
  • quadratic fields
  • unit group

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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