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What can primes, except 2, 3, and 5, be congruent to $\pmod {30}$? After some trials, I found out that a prime $p \gt 5$ is congruent to $q\pmod{30}$, where $q$ is also a prime, and $1 \le q \lt 30 \;$ (i.e.  $p \equiv q\pmod{30}.$  Is there a way to write a formal proof to show this?  Is that an acceptable answer. Natural Sort Order in C# Anyone have a good resource or provide a sample of a natural order sort in C# for an FileInfo array?  I am implementing the IComparer interface in my sorts. HDMI over cat extender video I'm actually at the cemetery at White Orchard. There is a white question mark and some little red arrows.  What are this little red arrows?  Do they point to something dangerous? How force Chrome to use google.com search engine without https Chrome's default search engine is .  How we can force chrome to use  without https?  I need a solution that allows proxies to rewrite my URLs, but https currently makes this impossible... Proving $\int_{0}^1\frac{x-1}{\log x}dx=\log 2$ and $\int_{0}^1\frac{\log x}{x-1}dx=\frac{\pi^2}{6}$ I would like to know how to prove the following two definite integrals.  A: $$\int_{0}^1\frac{x-1}{\log x}dx=\log 2$$  B:$$\int_{0}^1\frac{\log x}{x-1}dx=\frac{\pi^2}{6}$$  I found these two by using wolfram-alpha, but I can't prove them. I suspect that the following relations might be used.  $$\log 2=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots=\sum_{n=1}^\infty\frac{(-1)^{n-1}}{n}$$and$$\frac{\pi^2}{6}=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\cdots=\sum_{n=1}^\infty\frac{1}{n^2}$$  I need your help. I've read through the elementary proof of why there exists a solution $x$ to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$ for $p$ an odd prime. Is there a group theory generalization for this fact as well? I have an elliptic curve $E$ over $\mathbb{F}_{11}$ defined by $y^2=x^3+4x$ with the point at infinity $\mathcal{O}$  I have a divisor of $E$, defined by $$D=\left[(0,0)\right]+\left[(2,4)\right]+\left[(4,5)\right]+\left[(6,3)\right]-4\left[\mathcal{O}\right]$$  I know that $\text{deg}(D)=1+1+1+1-4=0$ and it is clear that $\text{sum}(D)=\infty$  Therefore $D$ is the divisor of a function - we want to find this function  I am given \begin{align}\text{div}(y-2x)&amp;=\left[(0,0)\right]+2\left[(2,4)\right]-3\left[\mathcal{O}\right]\\ \text{div}(x-2)&amp;=\left[(2,4)\right]+\left[(2,-4)\right]-2\left[\mathcal{O}\right] \end{align}  I am then told that we can express $D$ as follows:  $$D = \left[(2,4)\right]+\text{div}\left(\frac{y-2x}{x-2}\right)+\left[(4,5)\right]+\left[(6,3)\right]-3\left[\mathcal{O}\right]$$  However, when I expand this back out, I get the following:  \begin{align}D &amp;= \left[(2,4)\right]+\text{div}\left(\frac{y-2x}{x-2}\right)+\left[(4,5)\right]+\left[(6,3)\right]-3\left[\mathcal{O}\right]\\ &amp;= \left[(2,4)\right]+\text{div}(y-2x)-\text{div}(x-2)+\left[\left(4,5\right)\right]+\left[(6,3)\right]-3\left[\mathcal{O}\right]\\ &amp;= \left[(2,4)\right]+\left(\left[(0,0)\right]+2\left[(2,4)\right]-3\left[\mathcal{O}\right]\right)-\left(\left[(2,4)\right]+\left[(2,-4)\right]-2\left[\mathcal{O}\right]\right)+\left[\left(4,5\right)\right]+\left[(6,3)\right]-3\left[\mathcal{O}\right]\\ &amp;= \left[(0,0)\right]+2\left[(2,4)\right]+\left[(4,5)\right]+\left[(6,3)\right]+2\left[\mathcal{O}\right]-\left[(2,-4)\right] \end{align}  which clearly isn't equivalent to the original $D$ unless $$\left[(2,4)\right]+2\left[\mathcal{O}\right]-\left[(2,-4)\right]=-4\left[\mathcal{O}\right]$$  Can anyone either explain what I've done wrong or show me how I can obtain the above equation please    This question comes in three parts:   Step 1 - This one Step 2 -  Step 3 - Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$? How do you remove duplicates from a list whilst preserving order? escaping double quotes and percent signs (%) in cron The following command works from prompt but not from crontab.   grep abc  /var/log/messages | grep "`date '+%B %d'`" | mail -s"abc log of `hostname`" shantanu.oak+`hostname`@gmail.com   I need to add it to daily cron. Flexslider view preview working but not on actual page My block is not working for the flexslider: The images are not appearing, but the view preview does work.  I don't know if it is relevant, but a similar problem would happen with just a slideshow view, although one image would appear and it would not cycle.  Could jQuery be a problem?  The following is the actual page with the block that is not showing any images.        The following is the view preview, which works. Why are loops always compiled into "do...while" style (tail jump)? Can 'AMD-only' RAM really be restricted to AMD chipsets, and if so, why? How do you mock a Sealed class? can be quite a pain.  I currently favor an  to handle this, but something about just keeps feels weird.    So, What is the best way you mock sealed classes?  Java answers are more than welcome.  In fact, I would anticipate that the Java community has been dealing with this longer and has a great deal to offer.  But here are some of the .NET opinions: We know that $e^{\pi i} = -1$ because of de Moivre's formula. ($e^{\pi i} = \cos \pi + i\sin \pi = -1).$  Suppose we square both sides and get $e^{2\pi i} = 1$(which you also get from de Moivre's formula), then shouldn't $2\pi i=0$? What am I missing here? How to use xcolor to color a pgfplot How do I use xcolor to color a specific cell from a table in pgfplots? Is xcolor the best tool to use here? I'm trying to loop over a list of colors and color the cells in the column individually.  \documentclass{article} \usepackage{pgfplotstable,filecontents} \RequirePackage{listofitems} \usepackage{}  \begin{filecontents*}{test.csv}     ColA, ColB, ColC     0.17, 0.91, 0.67     0.15, 0.17, 0.92     0.48, 0.1, 0.28 \end{filecontents*}     \begin{document}     \pgfplotstabletypeset[col sep=comma,     ]{test.csv}     \def\mylistOne{green, blue, orange}     \readlist*\mylistTwo{\mylistOne}     \newcounter{myCounter}     \setcounter{myCounter}{-1}     \foreachitem\x\in\mylistTwo[]{         \stepcounter{myCounter}         \pgfplotstableset{             every row \themyCounter column 1/.style={                 \cellcolor{\x}         }     } } \end{document} i want to create new event in SharePoint calendar list in which I have some custom columns,i tried below code but it is not working      function bookingRoomForMeeting() {         var ctx = new SP.ClientContext(appWebUrl);//Get the SharePoint Context object based upon the URL           var list = ctx.get_web().get_lists().getByTitle("MyCalendarList"); //Get the List based upon the Title         var listCreationInformation = new SP.ListItemCreationInformation(); //Object for creating Item in the List         listItem = list.addItem(listCreationInformation);         listItem.set_item('Title', $("#txt_Title").val());         var date = $("#txt_startTime").val();         var dateTime = moment(date, 'DD/MM/YYYY HH:mm a').format("MM/DD/YYYY HH:mm a");         listItem.set_item('EventDate', dateTime);         var enddate = $("#txt_endTime").val();         var enddateTime = moment(enddate, 'DD/MM/YYYY HH:mm a').format("MM/DD/YYYY HH:mm a");         listItem.set_item('EndDate', enddateTime);         listItem.set_item('EmailId1', $("#txt_EmailId1").val());         listItem.set_item('EmailId2', $("#txt_EmailId2").val());         listItem.update();         ctx.load(listItem);         ctx.executeQueryAsync(             Function.createDelegate(this, success),             Function.createDelegate(this, fail)            );     } function success() {     alert("Completed"); } function fail() {     alert("operation failed"); }   list am using is SharePoint hosted app list,can any one tell me where am going wrong? Loopy integral $\int xe^x\sin(x)$ Question Tag problem! Question:     A man like you should not do this, _______?   Which question tag should I use in the blank space?   should he? should you?   Which would be grammatically correct? I think 1 is true.