Timeline for Jacobi symbols for two-square sums of primes
Current License: CC BY-SA 4.0
25 events
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| Mar 24 at 13:53 | comment | added | Alexey Ustinov | @GHfromMO I've added my reconstruction of Jacobsthal's argument as a separate answer. | |
| Mar 24 at 8:19 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 24 at 5:53 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 24 at 0:26 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 23 at 23:44 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 12 at 21:30 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 12 at 20:50 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 12 at 3:13 | comment | added | GH from MO | @RolandBacher I removed the reference to Barnes (1974), but added a detailed treatment in the "Added" section. I found the exposition in Jacobsthal (1907) too terse. | |
| Mar 12 at 3:08 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 12 at 2:45 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 12 at 2:39 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 12 at 2:21 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 12 at 2:14 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 11 at 13:09 | comment | added | Roland Bacher | Thanks for your great answer! (Concerning the Barnes proof : I remember having read it 30 years ago and there was a really stupid mistake with modular arithmetics (the type of mistake in all those marvellous proofs of the Fermat-Wiles Theorem).) | |
| Mar 11 at 13:03 | comment | added | GH from MO | @RolandBacher I don't know that. The brief MathSciNet review about Barnes' paper was written by Paul Erdős, but that of course does not mean much. Jacobsthal's proof should be reliable (and there was an earlier proof by Cauchy, presumably hard to read for us). BTW, I expect that one can also see from the analysis for $p\equiv 1\pmod{16}$ why the pattern breaks down for $p\equiv 1\pmod{32}$. Thanks for accepting my answer officially! | |
| Mar 11 at 13:01 | vote | accept | Roland Bacher | ||
| Mar 11 at 12:47 | comment | added | Roland Bacher | The proof by Barnes is fatally flawed if my memory is correct. | |
| Mar 11 at 1:56 | history | edited | Gerry Myerson | CC BY-SA 4.0 |
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| Mar 11 at 0:30 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 11 at 0:23 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 11 at 0:11 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 10 at 22:36 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 10 at 22:28 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Mar 9 at 18:26 | comment | added | Roland Bacher | Nice observation which shows a bit more: The odd number among $\lbrace A,B\rbrace$ is always a square modulo $p$. If $p\equiv 5\pmod 8$, then half of the even number (which is odd) is therefore also a square. | |
| Mar 9 at 18:11 | history | answered | GH from MO | CC BY-SA 4.0 |