How many positive factorials are also perfect Squares. So for example $1!=1=1^2$. How many others exist other than 1?  Is there any way to prove this?
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?  Clearly, when $n$ is prime, $n!$ is not a perfect square because the exponent of $n$ in $n!$ is $1$.  The same goes when $n-1$ is prime, by considering the exponent of $n-1$. What is the answer for a general value of $n$?  (And is it possible, to prove without Bertrand's postulate. Because Bertrands postulate is quite a strong result.)
Finite ring has only zero divisors and units If a nonzero element $a$ of a ring $\mathbb{D}$ does not have a multiplicative inverse, then $a$ must be a zero divisor.   If $\mathbb{D}$ has finitely many elements, then the statement is true. However, I don't see why, as for the infinite case, 7 isn't a zero divisor only because every element $a &gt; 0$ when multiplied by a $b &gt; 0$ gives you $ab &gt; 0$ which has nothing to do with infinity or finite amounts of elements. Limit of Multivariate Probability Density Function as one or more or all variables approach positive or negative infinity Could someone point out a good source or provide justification as to whether the limit of a multivariate probability density function, as one or more or all variables tends to positive or negative infinity, goes to zero.  $$\lim_{x_{1}\to\pm\infty}f(x_{1},x_{2},...,x_{n})=0$$  $$\lim_{x_{1},x_{2}\to\pm\infty}f(x_{1},x_{2},...,x_{n})=0$$  $$\lim_{x_{1},x_{2},...,x_{n}\to\pm\infty}f(x_{1},x_{2},...,x_{n})=0$$  I have found this related question for the univariate case: Which is grammatically correct?  I can only do so much in this time.  or  I can do only so much in this time. "Distribution worker" vs. "distributed worker" I cannot differentiate the meanings of the two words. Could you please clarify?   In general, when should I use a noun (distribution) or an adjective (distributed) for verbs similar to distribute, like organize, create? What is the "canary thread" and why is it starving? The following occasionally appears in /var/log/syslog:  rtkit-daemon[1145]: The canary thread is apparently starving. Taking action. rtkit-daemon[1145]: Demoting known real-time threads. rtkit-daemon[1145]: Successfully demoted thread 1431 of process 1368 (n/a). rtkit-daemon[1145]: Successfully demoted thread 1430 of process 1368 (n/a). rtkit-daemon[1145]: Successfully demoted thread 1368 of process 1368 (n/a). rtkit-daemon[1145]: Demoted 3 threads.   What's going on here? How to call child component controller function/helper from Parent Component Controller How to efficiently partition a single Windows-Ubuntu dual boot disk? This is not a question on  or  but is a question on access rights and how not to let them bite you in the lower abdomen...  ;-) This question will not help you how to make partitions on your disk, but will tell you what to do in , depending on your personal use case, so choose one of the following:      Note: The above questions can also be used with multiple disks, but the examples in the answers are given for one disk. What would be better practice when giving a function the original variable to work with:  unsigned long x = 4;  void func1(unsigned long&amp; val) {      val = 5;             } func1(x);   or:  void func2(unsigned long* val) {      *val = 5; } func2(&amp;x);   IOW: Is there any reason to pick one over another? "Prometheus" is meant to be a prequel to "Alien", happening 30 years before ().  If that's the case, how come one of the very earliest spaceships, Prometheus from 2089, has a spiffy new technology, while Nostromo has antique text based CRTs, mechanical IBM style keyboards, and all the associated technologies screaming "1980s called, and they want their IBM PC back!" ?  The great visuals of this can be seen in this Youtube Video  (ignore the russian voice-over - the guy is a movie critic who is complaining pretty much of the same discrepancy listed above).  Please note that I'm looking ONLY for in-universe answers (movies, scripts, explanations from creative team). I'm utterly un-interested in the obvious out of universe "well, for 1979 Alien film, 1980s technologies was the future, and 2012 movie is expected to look futuristic in 2012, duh" or speculations that make sense but aren't confirmed in canon.          And for those who don't believe me... to quote the immortal quip from Men in Black 2:   Old and busted:        New hotness: How to set QGIS language other then OS How many combinations of groups are there where no member of a group has been with another member before? I found this hard to word in the title, so let me give an example. I have 16 students, and I want to split them up into 4 groups of 4. However, I want to make sure that every time I have a new combination of groups, that a student has never been with any of their new groupmates before. I found info on how to separate objects into groups, but not in only unique ways as I've described above. I think I figured this out the rote way, by assigning each student a number and then finding the unique combinations, and got 3. But I'd like to know the math behind it, and how it could be applied to other configurations (20 students w/ 4 groups of 5?). Thanks for any help you can give! I want to find an example of a homomorphism $f:G\to H$ such that $A$ is a normal subgroup of $G,$ but $f(A)$ is not so in $H.$  I know that if $f$ was onto $f(A )$ must be normal , but otherwise i want to find an example! tikz arc with -latex arrow tip Why the arc does not fit over the circle if we use -latex arrow tip? Maybe some bug or some bad math computations?    MWE  \documentclass[11pt,margin=2pt]{standalone} \usepackage{tikz} \usetikzlibrary{arrows.meta}  \begin{document} \begin{tikzpicture} \draw         (0:1cm) arc (0: 180:1cm) arc (180:0:1cm and 2cm); \draw         (0:1cm) arc (0:-180:1cm); \draw[-&gt;]     (0:1cm) arc (0:  80:1cm); \draw[-latex] (0:1cm) arc (0:- 80:1cm); \end{tikzpicture} \end{document} Using global variables in a function How can I create or use a global variable in a function?  If I create a global variable in one function, how can I use that global variable in another function? Do I need to store the global variable in a local variable of the function which needs its access? Replace all occurrence of character except first one Jump/Scroll to selected object in the outliner? After installing Adobe PDF reader, it opens files with the .PDF file extension. Ones' default web browser opens .html files and notepad opens .txt files, etc.  Where exactly in the registry are these filetype - program associations stored in the registry?   In other words, how does Windows know with which software/program it must open a certain file(type)? Is there a single word with the same meaning as "good moments" or "pleasant memories"? I'm looking for a word which describes good thing(s) that happened to someone. The only word I can think of is "joy".  Some examples might be:   Wayne has many pleasant memories of the days spent with the family. She could remember many good moments from the last weekend. I need to run a query like:  SELECT p.id, p.name,         (SELECT name            FROM sites s           WHERE s.id = p.site_id) AS site_list   FROM publications p   But I'd like the sub-select to return a comma separated list, instead of a column of data.  Is this even possible, and if so, how? The recent  about a new supermassive virus being discovered got me thinking about how we define viruses as non-living organisms whilst they are bigger than bacteria, and much more complex than we first gave them credit for.   What biological differences between viruses and cellular organisms have made viruses be deemed non-living?