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prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$ Prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$  first im trying to proof if p is prime number there is positive integer n such that $p+1=n^2$ implies $p=3$  suppose there is positive n integer such that $p+1=n^2$ and prove that $p=3$. $p=n^2-1=(n+1)(n-1)$ since $p$ is prime $n-1=1$,$ n = 2 $ $p+1=4$ $p=3$ hence it is proved that $p=3$  now if $p=3$ implies there is positive integer n such that $p+1=n^2 $  $p=3$ and p is prime  $p+1=n^2$, $4=n^2$, $n2$ or $n=-2$ hence it is proved that there is positive integer $n$ such that $p+1=n^2 $  is my proof correct? and also for prime number can i write $n+1=1$ instead $n-1=1$? How do I open a terminal? Possible Duplicate:             I just got ubuntu running on my computer and now I am ready to write a program...but I can't figure out how to open a command terminal. I guess I don't know where to find which version I am running either. Any help would be appreciated. Thank you. Is there a rule of thumb for objective questions asked out of curiosity? Converting Polygon into single or all Points using QGIS? How do I check if a string contains a specific word? How to create a meta-package that automatically installs other packages? I'd like to be able to create a package that doesnt contain any code or programs itself, but instead installs other packages that exist in the repositories onto a computer, sort of how the ubuntu-restricted-extras package does? How to AutoSize the height of a Label but not the width Infinite set and countable subsets Prove that a set $A$ is infinite if and only if $A$ contains a countable subset $C$. I know I have to build a sequence and then I'll get a countable subset, but I don't know how to build that sequence from a infinite set. A story where technology is forbidden, but used by priests I am looking for a story I remember reading in the mid-90s. I can't remember if it was a trilogy or just a three part book, but I know it was in paperback book form. I also know it was found in the Young Adult section of the library at that time.  The general premise was that there had been some sort of war in the past and machines were outlawed. People visited priests who used magic. I remember that the main character discovers that the priest aren't using magic but are actually using machines.  I can also remember the main character ends up leaving the nation he is in and ends up in a neighboring nation where machines are allowed. I remember there being a scene where he watches a "movie" which I think was more like an old fashioned moving picture.  For some reason I keep wanting to tie this whole thing back to a sword, or blue sword, or something like that, but I might be mixing stories. Other things I keep linking to it: the character was in training to be a priest, he was forced to leave, he ended up using the neighboring nation to conquer his homeland. Again, still not sure if I am mixing things but they keep popping up.  I do know that it is not The Blue Sword by Robin McKinley, or its prequel, The Hero and the Crown. 2.81.16 No Rock Generator Say you have a stick which breaks randomly into three pieces (we can choose the points randomly). What is the probability that the area is greater than or equal to $0.4$?   I can see it has something to do with Heron's formula but I just can't put t together. I want to install Oracle's JRE and to update to the latest version with the Software Updater when they released. Is there a Ubuntu package that is provided by Canonical or Oracle?  Before release Java 7, I followed  to install Java 6.  But it doesn't work for Java 7. There is no package sun-java7-xxx. How can you install Java 7? How do I attach events to dynamic HTML elements with jQuery? Creating fillable PDFs I'd like to create a LaTeX document that when rendered into PDF, has forms that can be filled out using Adobe Reader or other such programs. Then I'd like to be able to extract the data. I deliberately would like to avoid using Acrobat for all the usual reasons (non-free, need different versions for different platforms etc).   Can this be done ? How to drive multiple LEDs from a Li-ion battery (with varying voltage)? How do I show that $X = \left\{ (x,y) \in \mathbb{R}^2 \mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\right\}$ is path connected?    Note that $X$ is a topological space with subspace topology $\tau = \left\{ U \cap X \mid U\text{ is open in }\mathbb{R}^2\right\}$.  I only know two things (with respect to path connectedness):   A topological space $X$ is path connected iff for every $p,q \in X$, there is a continuous function $f: [a,b] \to X$ with $f(a)=p$ and $f(b) = q$.    Continuity $f$ is defined as for every open set in $X$, its preimage is open in $[a,b]$ (with subspace topology induced by $\mathbb{R}$ (with standard topology) )   Suppose $X$ and $Y$ are two topological spaces and $f: X \to Y$ is a continuous surjection. If $X$ is path connected, then $Y$ is path connected. I am getting the error:   touch: cannot touch `/opt/tsrm/compliance/cme/log/20121207.log`: No such file or directory   on the touch command: touch $LOGFILE  I also checked the link: , But I didn't understand the answer.   Note: I was also getting mkdir: cannot create directory; I fixed this by adding the -p option.   Could this be something with the version of Linux I am working in? What does the term "BODMAS" mean? What is BODMAS and why is it useful in programming? Live USB "Check disk for defects” finds defects but doesn't list them I downloaded the iso file for XUbuntu. I created a live usb using Pen Drive Linux. I turned on my computer, booted to the XUbuntu installation screen, and selected "check disk for defects".  A minute later, it says that it found one defect. How do I figure out what this defect is? I was surprised recently to find that it's possible to have a return statement in a finally block in Java.  It seems like lots of people think it's a bad thing to do as described in ''. Scratching a little deeper, I also found '' which shows some pretty horrible examples of other types of flow control in finally blocks.  So, my question is, can anyone give me an example where a return statement (or other flow control) in a finally block produces better / more readable code?