On the number of solutions of the generalized Ramanujan-Nagell equation D1x2 + Dm2 = 2n+2

  • Jianghua Li
Keywords: Exponential diophantine equation, generalized Ramanujan-Nagell equation, number of solutions, upper bound

Abstract

Let D1, D2 be coprime odd integers with min(D1, D2) > 1, and let N (D1, D2) denote the number of positive integer solutions (x, m, n) of the equation D1x2 + Dm2 = 2n+2. In this paper, we prove that N (D1, D2) ≤ 2 except for N (3, 5) = N (5, 3) = 4 and N (13, 3) = N (31, 97) = 3.

Keywords: Exponential diophantine equation, generalized Ramanujan-Nagell equation, number of solutions, upper bound

Published
2018-04-03
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606