Gelfond–Schneider theorem: If a and b are algebraic numbers with a ≠ 0,1 and if b is not a rational number, then any value of ab is a transcendental number. -- Gene
________________________________ From: Adam P. Goucher <apgoucher@gmx.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, March 2, 2014 4:32 PM Subject: Re: [math-fun] Question about uniform distribution (mod 1) of a sequence
Vaguely plausible? They fall down at the obstacle of that theorem whose name I can't remember (and far too inebriated to Google) which states that (rational)^(algebraic) is transcendental.
Sincerely,
Adam P. Goucher
----- Original Message ----- From: Keith F. Lynch Sent: 03/02/14 11:19 PM To: math-fun@mailman.xmission.com Subject: Re: [math-fun] Question about uniform distribution (mod 1) of a sequence
Dan Asimov <dasimov@earthlink.net> wrote:
It was especially the famous case of 163 that got me thinking:
I first heard of it in Martin Gardner's Mathematical Games column in the April 1975 Scientific American, in which he claimed that exp(pi*sqrt(163)) had recently been proven to be an integer.
It was a joke article, and made several other equally false but vaguely plausible claims.
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