The continued fraction of (1 + [square root] D)/2 for certain infinite classes of D with applications to units and class numbers

We determine the continued fraction expansion of (1 + √D)/2 for all classes D considered by H.C. Williams (see [12]), C.L. Levesque and G. Rhin (see [7]), and C.L. Levesque (see [6]); for which D = 1 (mod 4) holds. From these continued fraction expansions we calculate the fundamental unit of Q(√D) in the case where D is squarefree. We deduce from the fundamental unit its norm and whether it is of the form a + b√D, a and b integral, or (a + b√D)/2, a and b odd. Finally, we apply a theorem of R.A. Mollin (see [8]) to determine a non-trivial lower bound for the classnumber of Q(√D) for a number of our classes D.