ACTA ARITHMETICA

On integer solutions to x2 − dy2 = 1, z2 − 2dy2 = 1 by P. G. Walsh (Ottawa, Ont.) 1. Introduction. Let d denote a positive integer. In [7] Ono proves that if the number of representations of d by the form 2a2 + b2 +8c2 equals twice the number of representations of d by the form 2a2 + b2 + 32c2, then the system of simultaneous Pell equations (1) x2 − dy2 = 1, z2 − 2dy2 =