Abu Muriefah, Fadwa S.Le, Maohua2024-07-012024-07-012021-11-110019-5588https://doi.org/10.1007/s13226-021-00197-3https://hdl.handle.net/11452/42622Let l be a fixed odd positive integer. In this paper, using some classical results on the generalized Ramanujan-Nagell equation, we completely derive all solutions (p, x, m, n) of the equation x(2) = 4p(n)-4p(m)+l(2) with l(2) < 4p(m) for any l > 1, where p is a prime, x, m, n are positive integers satisfying gcd(x, l) = 1 and m < n. Meanwhile we give a method to solve the equation with l(2) > 4p(m). As an example of using this method, we find all solutions (p, x, m, n) of the equation for l is an element of {5, 7}.eninfo:eu-repo/semantics/closedAccessPolynomial-exponential diophantine equationGeneralized ramanujan-nagell equationBaker's methodScience & technologyPhysical sciencesMathematicsMathematicsArticle00071739370000191592253410.1007/s13226-021-00197-3