Le, Maohua2024-09-172024-09-172023-01-130019-5588https://doi.org/10.1007/s13226-023-00372-8https://hdl.handle.net/11452/44816Let k be a fixed positive integer with k > 1. In this paper, using various elementary methods in number theory, we give criteria under which the equation x(2) + (2k - 1)(y) = k(z) has no positive integer solutions (x, y, z) with y is an element of {3, 5}.eninfo:eu-repo/semantics/closedAccessPolynomial-exponential diophantine equationGeneralized ramanujan-nagell equationElementary method in number theoryScience & technologyPhysical sciencesMathematicsArticle00091372410000139239955110.1007/s13226-023-00372-8