I am trying but still unsuccessfully solving the following question:  For every positive integer $n$, show that any prime divisor of $12n^2 + 1$ is of the form $6k + 1$, where $k$ is an integer.  I would like, if possible, to get a solution that does not refer to Legendre symbol or quadratic reciprocity. That is: I would like to get, if possible, a more elementary solution.  I ask for help.
Let $n$ be an integer, prove that every prime factor of $12x^2+1$ has the form $6m+1$, where $m$ is an integer.  I've gone as far as knowing that all primes $p&gt;3$ are either $6m+1$ or $6m-1$, how do I use this, not sure whether to even use that.  I know about the Legendre symbol and quadratic reciprocity
How did Sauron remain in control of the Nazgûl? What are FML and BWSS? I see this ad sometimes and I would like to know what the acronyms are. rtl8723ae unstable on Ubuntu 14.04 I have searched through the internet and in AskUbuntu, but I could not find a working solution for my little problem.  The RTL8723ae WLAN is behaving strangely on Ubuntu 14.04 and drops the WLAN connection constantly. I am using the notebook MSI GE40 and have already seen on the web that there are other people having the same problem but there was no permanent solution. The problem did not exists on the original Windows 8 on the device and the router is a TP-Link, which I can control (channel change and so on, I use WPA2-PSK WLAN security). wireless network adapter supported on ubuntu? Disable Ctrl+Alt+Del on Windows 7 What's recommended for the number of users to use in qualitative and quantitative testing? Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$. 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What do I need to do to reference them and what issues might it create when upgrading to the next version?  If there is no way except for building from source, is there a (pseudo) package that I can can install that will provide all of the dependencies needed without having to find and install each individually? So that I don't get:  The necessary bits to build these optional modules were not found: _bz2                  _curses               _curses_panel       _dbm                  _gdbm                 _lzma               _sqlite3              _ssl                  _tkinter            readline              zlib Let $a_1,\dots ,a_n \in \mathbb{R}^n$ with $a_i = (a_{i1}, \dots , a_{in})$.  Show that when $\mid a_{jj}\mid \gt \sum_{i \neq j} \mid a_{ij} \mid \; \forall \; j\in \{1,\dots ,n\}$, then $a_1,\dots ,a_n$ are linearly independent.  I want to show that the matrix \begin{matrix} a_{11} &amp; a_{21} &amp; \cdots &amp; a_{n1} \\ a_{12} &amp; a_{22} &amp; \cdots &amp; a_{n2} \\ \vdots &amp; &amp; \ddots &amp; \\ a_{1n} &amp; a_{2n} &amp; \cdots &amp; a_{nn} \end{matrix} can be transformed into an upper triangular matrix with all entries in the main diagonal $\neq 0$.  For the cases $n=1$ and $n=2$ this is easy. However, I fail to show this for the general case; the problem being that the tranformations mess up the coefficients such that I can't use the assumption on the $a_{jj}$'s anymore.  I'm pretty sure that this has already been solved somewhere on here, but I don't know how to search for it. I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. 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Here is what I did (I think there could have been a better way to do this)     $(p \lor q ) \land (\neg((p \Rightarrow q) \land (q \Rightarrow p)))$ breaking of output into new lines Android : Is there any alternative to listFile function (Android java.io.File.listFiles()) A correct preposition - account closed due/by/at 12th of May Can I run CAT5/6 cables parallel to electrical cables? How do you compile OpenSSL for x64? After following the instructions in INSTALL.W64 I have two problems:   The code is still written to the "out32" folder. I need to be able to link to both 32-bit and 64-bit versions of the library on my workstation, so I don't want the 64-bit versions to clobber the 32-bit libs. The output is still 32-bit! This means that I get "unresolved external symbol" errors when trying to link to the libraries from an x64 app. $\delta$ differential notation Various textbooks that I am currently consulting (including Spacecraft Dynamics and Control An Introduction - Anton H.J. De Ruiter | Christopher J. Damaren | James R. Forbes Section 1.4, page 32) use $\delta$, not $d$ or $\partial$ to express an infinitesimal quantity. In the context of the reference text above, the symbol is used as part of a general definition for the derivative of a vector. Specifically, given   $$\mathbf{\vec{r}}=\mathcal{\vec{F^{T}_{1}}}\mathbf{\vec{r_{1}}}$$   where   $$\mathcal{\vec{F^{T}_{1}}}$$   is a vectrix   $$[\mathbf{\vec{x_1}} \phantom{s} \mathbf{\vec{y_1}} \phantom{s} \mathbf{\vec{z_1}}].$$  The time derivative of the vector is defined as   $$\dot{\mathbf{\vec{r}}}\triangleq \lim_{\delta t\to 0}\frac{\delta\mathbf{\vec{r}}}{\delta t}.$$  In this context, what is the difference between $\frac{\delta\mathbf{\vec{r}}}{\delta t}$ and $\frac{d \mathbf{\vec{r}}}{d t}$ ?  Note about thermodynamic use of $\delta$: My understanding is that $\delta$ is used in thermodynamic equations to express path dependence of a scalar quantity such as heat or work. What does it mean in the context of an abstract physical vector? I just signed up, a day or two ago, and I've received a notification that there's something in my inbox.  Unfortunately, my email client isn't able to show me a link to my Inbox, or the message, because of the format of the email.  I normally use the email address that I gave when I signed up, just with MailWasher, which is intended to safely preview emails, as plain text, to decide whether or not to open them in a normal HTML email client.  I would be nice if that email contained a link to my inbox, which could be shown in MailWasher.  In order to collect that email in a normal email client, I'd also have to collect or delete all the other emails sent to that address.  I'm not entirely clear what's been done in that email to stop MailWasher seeing the link.  I can see a link to leave feedback, and one to unsubscribe, but not one to check my inbox.  Sure, I can live without one, but those emails would be a lot more useful to me if I could just click a link to go to my Inbox.