CERTAIN REAL QUADRATIC FLELDS WITH CLASS NUMBERS 1, 3 AND 5

The quadratic fields generated by $x^2$=ax+1($\alpha\geq$1) are studied. The regulators are relatively small and are known at one. The class numbers are relatively large and easy to compute. We shall find all the values of p, where p=$\alpha^2$+4 is a prime in $\mathbb{Z}$, such that $\mathbb{Q}(\sprt{p})$ has class numbers 1, 3 and 5.