
Re: Independent sqaure roots???
Posted:
Apr 30, 2003 6:14 PM


"Chris Hughes" <hughes@post.tau.ac.il> wrote in message news://4e5b4dbf.0304301333.7f51f5c2@posting.google.com... > David C. Ullrich <ullrich@math.okstate.edu> wrote in message news:<91cvav4jl262v76q6elt4fh5oj3hrknub5@4ax.com>... > > Are the square roots of the positive squarefree 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 > squarefree integers are linearly independent over the rationals". > This comes from page 405 of a paper of HeathBrown in Acta > Arithmetica, 60 (1992) 389415. 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, 36.
HTH, Paul

