General Ramanujan-Type Diophantine Equations and Their Complete Solution Original Research Article

Ramanujan′s equation x2 + 7 = 2n + 2 is generalized in a natural way to the form B2n + 7A2n = 2n + 2, and its complete solution is given. Within this class of equations Ramanujan′s equation becomes a special case, and all the results obtained apply to it. The generalized equation is rich in producing interesting results, among them many recursion relations. We do not think that the consequences of it are still exhausted.