Timeline for Is it possible to find a (nonsquare) integer which is a quadratic residues modulo a given infinite list of primes?
Current License: CC BY-SA 4.0
9 events
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| Aug 27, 2020 at 19:21 | comment | added | Joshua Holden | (In particular this shows how to explicitly construct a sequence of integers $d_n$ that work for larger and larger $n$, and that seems like the next best thing. I'm still wondering if there's a single $d$ that works but I admit now that it seems unlikely!) | |
| Aug 27, 2020 at 19:13 | vote | accept | Joshua Holden | ||
| Aug 27, 2020 at 19:12 | comment | added | Joshua Holden | Ah, I see. Thanks for the update! I hadn't thought about the properties of generalized Fermat numbers before. It turns out -1 doesn't quite work for the application I wanted (see edit) but this gives me something I can work with! | |
| Aug 20, 2020 at 18:43 | comment | added | Aaron Meyerowitz | In those now deleted lines I took $p=3$ since it was small and $7$ as a prime which is $1 \bmod 2p.$ I was probably confused and thinking of this fact: The prime factors of $2^p-1$ are all $1 \bmod 2p.$ So you might be able to get results for certain instances of "the list of all prime factors of $2^p-1$ where $p$ is a prime congruent to $u \bmod v.$" But, again, only because that restricts congruence classes $\bmod 2d.$ | |
| Aug 20, 2020 at 18:23 | history | edited | Aaron Meyerowitz | CC BY-SA 4.0 |
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| Aug 20, 2020 at 3:42 | comment | added | Joshua Holden | Thanks very much, Aaron! In your example, I'm assuming that you took $p=3$ and $d=7$ just as convenient small numbers? | |
| Aug 17, 2020 at 5:15 | history | edited | Aaron Meyerowitz | CC BY-SA 4.0 |
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| Aug 17, 2020 at 3:51 | history | edited | Aaron Meyerowitz | CC BY-SA 4.0 |
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| Aug 17, 2020 at 3:06 | history | answered | Aaron Meyerowitz | CC BY-SA 4.0 |