Timeline for What are some examples of ingenious, unexpected constructions?
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6 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2012 at 20:18 | comment | added | roy smith | some people may also find the usual one sentence proof ingenious: If p = 4k+1 is prime, the residue -1 has the four square roots ±i, ±(2k)! in Zp[i], whence Zp[i] = Z[i]/(p) is not a domain, so since Z[i] is a ufd, p factors there as p = (a+bi)(c+di), thus p^2 = (a^2+b^2)(c^2+d^2) in Z, and p = a^2 + b^2. | |
| Mar 12, 2012 at 10:30 | comment | added | Lennart Meier | It must be mentioned that it is just an (admittingly ingeniuos) contraction of a more natural proof using three involutions (which can be found, for example, in proofs from the BOOK). | |
| Mar 12, 2012 at 9:31 | comment | added | Martin Brandenburg | people.mpim-bonn.mpg.de/zagier/files/doi/10.2307/2323918/… | |
| Mar 12, 2012 at 0:11 | comment | added | eventually | can you please add the one sentence proof? | |
| Mar 11, 2012 at 17:37 | comment | added | Robert Kucharczyk | That is a great example: it is ingenious and totally non-straightforward. | |
| Mar 11, 2012 at 17:10 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |