On some generalized Lebesgue-Nagell equations

By using known results and elementary arguments, we give all solutions of some generalized Lebesgue-Nagell equationsx2+qm=yn,x,y,m,n∈N,n⩾3,q∈{11,19,43,67,163}, where the class number of the imaginary quadratic field Q(−q) is one.