An efficient algorithmic solution of the Diophantine equation $u\sp{2}+5v\sp{2}=m$

The determination of irreducible elements of the domain $Z[\sqrt { - 5} ]$ requires the solution of the Diophantine equation ${u^2} + 5{v^2} = m$, where m represents certain primes or products of two primes. An algorithm of order $\log m$ is given for the solution of the equation.