Abstract
In this paper it has been proved that if q is an odd prime, q≢7 (mod 8), n is an odd integer ⩾5, n is not a multiple of 3 and (h,n)=1, where h is the class number of the filed Q(√−q), then the diophantine equation x2+q2k+1=yn has exactly two families of solutions (q,n,k,x,y).