This paper treats the diophantine equation dV2 - 2eVW - dW2 = 1, where d and e are positive integers, by methods using the arithmetic of the ring of the gaussian integers.

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Journal Pacific Journal of Mathematics
Hardy, K. (Kenneth), & Williams, K.S. (1986). On the solvability of the diophantine equation dv2 - 2evw - dw2 = 1. Pacific Journal of Mathematics, 124(1), 145–158.