Abstract

AbstractLetDbe a nonsquare integer, and letkbe an integer with |k| ≥ 1 and gcd(D,k) = 1. In the partIof this paper, using some properties on the representation of integers by binary quadratic primitive forms with discriminant 4D, M.-H. Le gave a series of explicit formulas for the integer solutions (x,y,z) of the equationx2–Dy2=kz, gcd(x,y) = 1,z> 0 for 2 ∤kor |k| is a power of 2. In this part, we give similar results for the other cases ofk.

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