The ternary exponential Diophantine equation concerning Pythagorean triplets

  • H Di
  • Z Wenpeng
Keywords: Ternary exponential Diophantine equation, Pythagorean triplet, Gel′ fond-Baker method

Abstract

Let r be a positive integer with r > 1, and let m be a positive even integer. Further let a = |V (m, r)|, b = |U(m, r)| and c = m2 + 1, where V (m, r) + U(m, r) √-1 = (m + √-1)r. In this paper, using the Gel′ fond-Baker method, we prove that if 2 | r and m > max(1015, 2r3), then the equation ax + by = cz has only the positive integer solution (x, y, z) = (2, 2, r).

Keywords: Ternary exponential Diophantine equation, Pythagorean triplet, Gel′ fond- Baker method.

Published
2016-08-11
Section
Articles

Journal Identifiers


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