title: The exponential Diophantine equation 2 x + b y = c z.
abstract: Let b and c be fixed coprime odd positive integers with min{b, c} > 1. In this paper, a classification of all positive integer solutions (x, y, z) of the equation 2 (x) + b (y) = c (z) is given. Further, by an elementary approach, we prove that if c = b + 2, then the equation has only the positive integer solution (x, y, z) = (1,1, 1), except for (b, x, y, z) = (89,13,1, 2) and (2 (r) - 1, r + 2,2, 2), where r is a positive integer with r ≥ 2.
authors: Luoyang Institute of Science and Technology, Luoyang, Henan 471023, China.
authors: Yahui
authors: Y
authors: Yu
authors: School of Mathematics, Northwest University, Xi'an, Shaanxi 710127, China.
authors: Xiaoxue
authors: X
authors: Li
mesh_terms: D008962:Models, Theoretical