> I don't have an answer to your question, but here is another statement
> about FLT attributed to Hilbert by S. Singh and K. Ribet in "Fermat's Last
> Stand", Sci. Amer., November 1997, p. 69 (they do not give a source).
> Hilbert made it in response to a question (it does not say who asked it)
> about why he never attempted a proof of FLT:
>
> Before beginning I should have to put in three years of intensive
> study, and I haven't that much time to squander on a probable
> failure.
See also: Simon Singh: Fermat's Last Theorem.
London: Fourth Estate, 1998, pp. 226 - 7
Quoting Singh (op. cit., pp. 267 - 8):
<q>
Back in 1920 David Hilbert, then aged fifty-eight, gave a public lecture in
Go"ttingen on the subject of Fermat's Last Theorem. When asked if the problem
would even be solved, he replied that he would not live to see it, but perhaps
younger members of the audience might witness the solution.
</q>
Probably in the same lecture he gave the "golden egg" answer.
Antreas