Abstract. We obtain a formula which expresses the square of the number of solutions of certain equations of the form $Ax^2+Cy^2=N$ in terms of the number of solutions of the equations $Ax^2+Cy^2=d$ and of the number of primitive solutions of the equations $ACx^2+y^2=d$, where $d$ runs through all the divisors of $4ACN$.

AMS Subject Classification (1991): 11D09

Received April 20, 1995 and in revised form March 9, 1996. (Registered under 6122/2009.)