A continued fractions approach to a result of Feit

For primes that can be written as a sum of integer squares, p = asup2 + (2b)sup2, Kaplansky asked whether the binary quadratic for F = xsup2 - pysup2 always represents a and 4b. Feit and Mollin proved the F does always represent a and 4b using the theory of ideals and the class group structure of quadratic orders. Here, Robertson and Matthews present a mathematical approach showing that a standard continued fraction methods give a more elementary answer to Kaplansky's question than the solutions by Feit and Mollin