On a Conjecture Concerning the Generalized Ramanujan-Nagell Equation

摘要

Let c be a fixed positive integer with c > 1. In 2014, N. Terai conjectured that the equation x~2 + (2c - 1)~y = c~z has only one positive integer solution (x, y, z)= (c - 1,1,2). Although this conjecture has been confirmed in some special cases, it is still a far from solved problem in the general case. For any positive integer N, let f(N) denote the number of c's which make Terai's conjecture hold with c 0.78.