Allan, I just asked essentially the identical question to math-fun a few weeks ago, under a subject line something like "Unsolved number theory problem". There were some interesting responses. —Dan -----Original Message-----
From: Allan Wechsler <acwacw@gmail.com> Sent: May 30, 2018 3:04 PM To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] "I don't find this proof beautiful" quote?
Is there any progress on the sum-of-three-cubes problem? I think 33 is the smallest number for which the answer is not known.
On Wed, May 30, 2018 at 5:29 PM, Mike Stay <metaweta@gmail.com> wrote:
:D https://cs.uwaterloo.ca/journals/JIS/VOL6/Broughan/broughan25.pdf
On Wed, May 30, 2018 at 2:54 PM, Bill Gosper <billgosper@gmail.com> wrote:
On 2018-05-29 09:59, Mike Stay wrote:
My favorite irrationality proof is one I heard from John Baez. Suppose the cube root of two were not irrational; then there would be two positive integers p, q such that p/q = ∛2. Multiplying both sides by q and cubing, we get p³ = 2q³ = q³ + q³, which has no solutions in the positive integers by Fermat's Last Theorem!
I just read this aloud to Rohan, who remarked "You can also use that for ∛9.", barely looking up from his video game. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.math.ucr.edu/~mike http://reperiendi.wordpress.com
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