David Speyer gave a beautiful application of the pigeon hole principle here to show that Pell's equation $$x^2-Dy^2=1$$ has infinitely many integral solutions.
I was wondering if anybody knows the history/origin of this argument...In particular was this the original argument used by Lagrange? Or was it Dirichlet? Or is this argument an original due to Speyer? Thanks!
PS I am not looking for alternative proofs of the solvability of Pell's equation...just comments on the proof given above.