Proving the divisibility of $4[(n-1)!+1]+n$ by $n(n+2)$ in the condition of $n,n+2 \in P$ where $P$ is the set of prime numbers
Wilson and Fermat's Theorem
The latest updates (4/1/2018) make my laptop constantly crash the GUI/Unity:  (Intel Pentium su4100 processor)  syslog:  Jan  5 11:38:53 1810 kernel: [ 1850.327738] compiz[11911]: segfault at 0 ip 00007f6c7baf0c16 sp 00007ffd5ec71c60 error 4 in i965_dri.so[7f6c7b513000+82d000]   After login I end up with an empty desktop, just a wallpaper, GUI/Unity are in a crash loop:   No panel.  No dash.  Can't start a program. Launcher disappears. Sidebar disappears. System crash. Windows key not working. The key combination Alt+Tab not working.   Simply, the computer is not usable. Same for guest login. The only thing working: open up a terminal CTRL+ALT+T to examine log files.  I somehow forced  to let me log in and file the bug, but still lots of problems:   Dash not working Alt+Tab not working Sometimes windows all disappear for a few seconds     Any ideas for a solution or workaround?   UPDATE     If you have the same/ very similar problems, follow the link to my    report and mark there that you're affected too. Or file your own. Please leave a comment   if you wish, or upvote - this is a nasty problem - but an answer should   offer a fix or a workaround so users can use their computer again.    Without , Ubuntu can't fix issues. How do I restore the default repositories? There are now errors when updating and I cannot install most software due to a corrupted  /etc/apt/sources.list   file. Is there a copy I can download to replace it?  The file would be for Ubuntu 12.04 (Final Beta) in the United States. OpenSource ATI driver - Fan running at full speed all the time I know this is a common problem and have read other topics but couldn't resolve. Anyways yesterday I found a solution - I have 2 graphic cards (hybrid) and they were both on. So I turned one off and installed Jupiter for power management and from there on the fans were quiet and I was happy as hell.  However (:)), yesterday evening I also updated the system and the fan and it's noise came back. I checked whether I am using only 1 graphics card and I am.  c0dehunter@mintBox ~ $ sudo lshw -c video [sudo] password for c0dehunter:    *-display                       description: VGA compatible controller        product: RS780M/RS780MN [Mobility Radeon HD 3200 Graphics]        vendor: Hynix Semiconductor (Hyundai Electronics)        physical id: 5        bus info: pci@0000:01:05.0        version: 00        width: 32 bits        clock: 33MHz        capabilities: pm msi vga_controller bus_master cap_list rom        configuration: driver=radeon latency=0        resources: irq:18 memory:c0000000-cfffffff ioport:c000(size=256) memory:fbcf0000-fbcfffff memory:fbb00000-fbbfffff   Maybe the problem is (false) temp reading from GPU?  c0dehunter@mintBox ~ $ sensors acpitz-virtual-0 Adapter: Virtual device temp1:        +44.0°C  (crit = +105.0°C)  k10temp-pci-00c3 Adapter: PCI adapter temp1:        +47.0°C  (high = +70.0°C)                        (crit = +115.0°C, hyst = +110.0°C)  radeon-pci-0200 Adapter: PCI adapter temp1:       +127.5°C     The thing that is weird is that if I boot into Windows the fan is still at full power (previously it wasn't). Did I f--- up my hardware with software? :)  //OH, yes - I forgot to mention that my laptop is not hot at all. The temps are about 50°C. Suppose $R\neq 0$ is a commutative ring with $1$. Let $M$ be a free $R$-module. I would like to prove that $M$ is a flat $R$-module. Everywhere I have looked (mostly online) this is proved by first proving that every free module is projective, and then proving that every projective module is flat. Unfortunately, Atiyah &amp; Macdonald's "Introduction to Commutative Algebra" (Chapter 2) does not discuss projective modules. But the result that every free module is flat comes very handy in the exercises.   So my question is,     Is it possible to prove that every free module is flat just by   definitions and without appealing to projective modules?   Thanks! Overlapping matches in Regex I can't seem to find an answer to this problem, and I'm wondering if one exists. Simplified example:  Consider a string "nnnn", where I want to find all matches of "nn" - but also those that overlap with each other. So the regex would provide the following 3 matches:   nnnn nnnn nnnn   I realize this is not exactly what regexes are meant for, but walking the string and parsing this manually seems like an awful lot of code, considering that in reality the matches would have to be done using a pattern, not a literal string. Complete Statistic: Uniform distribution Take a random sample $X_1, X_2,\ldots X_n$ from the distribution $f(x;\theta)=1/\theta$ for $0\le x\le  \theta$.  I need to show that $Y=\max(X_1,X_2,...,X_n)$ is complete.  Now, I know I should multiply the sample distribution of $Y$ and multiply it with a function of $Y$, then integrate over the range of $\theta$ and equate them to zero. But how do I get the sampling distribution of $Y$? A book suggests that we should not interchange "so" and "so that". "So" means "therefore", and "so that" means "in order that". However, it seems to me that in many cases they don't actually have a difference. For example:     Alice got up at 5:00 A.M., so that she could drive her son to school.   If I substitute "so that" with "so", this sentence presents the exact same causal relation to me:     Alice got up at 5:00 A.M., so she could drive her son to school.   I must have missed something here, since English is my second language. Could somebody explain the difference? proving that $f(x) = x^s$ is holder continuous with holder exponent s I understand test -n &lt;expression&gt; to return false if the expression evaluates to a string length of greater than 0.  Why then does the following happen?  Macbook:~ echo ${#undeclared_variable} 0 Macbook:~ test -n $undeclared_variable &amp;&amp; echo Foo Foo   Bash 4.x  My expectation is that since test -n $undeclared_variable should evaluate false, that Foo should not be echoed.  If I use [[  ]] instead of test, it works as expected. How can I search for a keyword with special characters in Google Search? I want to search for what += means, but Google won't return any documents.  Also when I come across some PHP code I don't understand I can't search for the keywords as written.  How can I search for these special characters or include these special characters in a search. Money - Countable or Uncountable noun page suggests that we use much with only uncountable nouns whereas the use of many/several is limited to countable nouns only. So I conclude that money is uncountable noun as I've heard people saying phrases like      So much money!   But, We do count the money in our daily life then why is it that money is considered an uncountable noun instead of countable? What if I say      I have $500 to spend   Wouldn't the money be considered countable in this case?  Edit The question may be considered duplicate of the suggested question but, in my opinion, the question on that link itself is not answered properly. How to prove that center of $GL_n(\mathbb R)$ is scalar matrices?  Again what can you say about the center of set of all upper triangular matrices and center of set of all diagonal matrices. I wanted to align a set of equations to left. I found on the Internet that you can do it easily with align* environment.   I found it here:   So I did it:  \begin{align*}  f(b)-f(a)=&amp;f((b_1,b_2,\dots,b_k))-f((a_1,a_2,\dots,a_k))=\ &amp;=\sum_{i=1}^{k}[f((a_1,\dots,a_{i-1},b_i,\dots, b_k))-f((a_1,\dots,a_i,b_{i+1},\dots, b_k))  \end{align*}   Unfortunately, I got bunch of red errors saying that there are missing $s. Why? Doesn't that align* environment provide a math environment already? How to tell the difference between linear and non-linear regression models? $P[X=x]=0$ when $X$ is continuous variable I was shooting the lighting of the city that is visible at the top of the trees if you shoot landscape.  No matter what I do, the image is blurry. What have i done:   ISO 100 Manual focus towards infinity Using a tripod Using really sharp prime &amp; good camera   Basically, everything I could. The only example i have is here, but it is not good, because image is underexposed:    The main question: Why can't night photographs be as sharp as daily photographs (with approperiate exposure times of course)? How to fix "W: Duplicate sources.list entry"? Does an Indian citizen need a transit visa in Australia? Indian passport holder. Do I need transit visa in Sydney? Hot and Week tabs not shown to non-logged in users (except on SO) Why do wet objects become darker?