"Chris Hughes" <email@example.com> wrote in message news://firstname.lastname@example.org... > David C. Ullrich <email@example.com> wrote in message news:<firstname.lastname@example.org>... > > Are the square roots of the positive square-free integers > > (including 1) linearly independent over Q? > > > > <snip> > > I see that this has already been answered above with a proof, but I > have previously seen this result quoted as "a classical result of > Besicovich, [which states] that the square roots of distinct > square-free integers are linearly independent over the rationals". > This comes from page 405 of a paper of Heath-Brown in Acta > Arithmetica, 60 (1992) 389--415. Unfortunately, he doesn't give a > reference to the original Besicovich paper. > > Chris Hughes
I haven't looked it up to make sure, but I'd guess it is the following:
A.S. Besicovitch (1940). On the linear independence of fractional powers of integers. J. London. Math. Soc. 15, 3-6.