On Solutions of Indefinite Binary Quadratic Form au2 + buv + cv2 = m

Copyright c © 2014 Bahar Demirtürk Bitim and Ece Özel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we consider solutions of indefinite binary quadratic forms. Firstly we obtain all integer solutions of the form u2−5uv+v2 = −3, then we find integer solutions of the most general binary quadratic form au2 + buv + cv2 = m by using the Pell equation x2 − dy2 = N, where a, b, c ∈ Z and m,N are nonzero fixed integers