On the Generalized Ramanujan–Nagell Equation x2+D=pz Original Research Article

Let pset membership, variant{3, 23} and Dset membership, variantimage such that p does not divide D and (D, p)≠(2, 3). We prove in this paper that the diophantine equationimage has at most one solution (x, z). Moreover, we give an explicit upper bound for z.