Puzzle: How far can we take this idea? It obviously applies to cbrt7 as well, and to 2^(1/n) for n>=3. We can also go from "cbrt9 is irrational" to "cbrt3 is irrational". Rich --------------- Quoting Bill Gosper <billgosper@gmail.com>:
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