See Nagell, Introduction to number theory, Theorem 107. Originally it was proved by Legendre, see Dickson, L. E. History of the theory of numbers. Vol. II, p. 365. There are more examples due to Dirichlet, see Dirichlet's Werke, Bd. 1 (1889), pp. 219-236.
An extended bibliography on negative Pell’s equation can be found in Gerasim, I.-Kh.I. On the genesis of Redei’s theory of the equation $x^2 -Dy^2 =-1$. (Russian) Zbl 0731.01014 Istor.-Mat. Issled. 32/33, 199-211 (1990).