LAUSR

Let [Formula: see text] be an imaginary quadratic extension of [Formula: see text]. Let [Formula: see text] be the class number and [Formula: see text] be the discriminant of the field [Formula: see text]. Assume [Formula: see text] is a prime such that [Formula: see text]. Then [Formula: see text] splits in [Formula: see text]. The elements of the ring of integers [Formula: see text] are of the form [Formula: see text] if [Formula: see text] and [Formula: see text] if [Formula: see text], where [Formula: see text] and [Formula: see text]. The norm [Formula: see text] and [Formula: see text], respectively. In this paper, we find the elements of norm [Formula: see text] explicitly. We also prove certain congruences for solutions of norm equations.