How can I prove that if $2^x+1$ is prime, then $x$ is a power of $2$? Can someone help me prove this?
A little bird told me that if $2^n+1$ is prime, then $n$ is a power of $2$. I tend not to trust talking birds, so I'm trying to verify that statement independently.  Suppose $n$ is not a power of $2$. Then $n = a \cdot 2^m$ for some $a$ not a power of $2$ and some integer $m$. This gives $2^n+1 = 2^{a \cdot 2^m}+1$. Now I suspect there's a way to factor that, but I don't see how. Can someone give me a hint?
Square bracket notation for dimensions and units: usage and conventions When transiting between two flights, will my luggage be automatically transferred? How to add field history and product as a related list of opportunity in vf page I am trying the below code to add field history and product as a related list of opportunity in vf page, but its not working .  &lt;apex:relatedList list="OpportunityFieldHistory"/&gt; &lt;apex:relatedList list="Product"/&gt;   Can anyone tell me what is the correct way to write it.  Regards    Edit:  There are two Standard objects that have Opportunity history information,  and . The relatedList component works fine with a value of OpportunityHistories for the list attribute, but an error is thrown when using the value of Histories, even though the SObject describe information shows "Histories" as the child relationship name.   &lt;apex:relatedList list="OpportunityHistories"/&gt; &lt;!-- Works fine --&gt; &lt;apex:relatedList list="Histories"/&gt;            &lt;!-- Error --&gt; Short connection at IAD (Dulles international airport) I am flying from New Orleans to Dulles (IAD) on United Express, and from IAD to Frankfurt on United. I have a short connection (45 minutes) in IAD.   I'm trying to figure out how can I make it:  Will I need to go throughout security and border check since I'm leaving the US? How big is IAD airport? and are there different terminals for domestic and international flights? If so, how long would it take to walk between them? Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2 Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $ I am trying to prove:     $a\mid b \land b\mid c \Rightarrow a\mid c $   $a\mid b$ means that a divides b if there is an integer k, that $b=k\cdot a$  Please give me a hint on how to start, because I have no idea. Decoupling caps, PCB layout How to change the Play Store language? Unable to cover get set in apex test class Drush 6 works great of corse on a Drupal 6 website, but will I have all of the Drush 6 features when working on a Drupal 7 website? Should I use Drush 7 when working on a drupal 7 website?  I found this post that says you can switch between the two version easily, is this correct?  switch to drush6 command: composer global require drush/drush:6.*  switch to drush7 command: composer global require drush/drush:dev-master I am a girl in my early twenties traveling to USA from India and in my visa application I have provided the contact address for a relative in San Francisco, and their invitation letter. I would like to visit LA first. Will I face problems during immigration if I land in LA (with an immediate on wards ticket to SF)? I dont plan to get on the flight from LA to SFO.  Initially I was planning to fly to SFO from India and then fly to LA immediately after completing immigration at SFO airport. Ideal charging / discharging percentage for maximum battery life? One of my friends has a relatively new Samsung smartphone. He has this app that notifies him whenever the charging is up to 80%, and tells him to unplug the charger.  He tells me that it will increase the number of charging cycles for his battery. He says that if he lets it charge all the way up to 100%, it will mean he has to replace the battery of the phone more often.  Is this true?  Somehow, I feel this is a thing of the past. I thought the internal architecture of batteries these days was made so that it wouldn't drop too low or too high. (In other words, when the phone is at 100%, it isn't really 100%. It's what the battery can safely be charged to in order not to degenerate too much.)  Here's a  which taught me something about this. I have studied that every normed space $(V, \lVert\cdot \lVert)$ is a metric space with respect to distance function  $d(u,v) = \lVert u - v \rVert$, $u,v \in V$.   My question is whether every metric on a linear space can be induced by norm? I know answer is  no but I need proper justification.   Edit: Is there any method to check whether a given metric space is induced by norm ?  Thanks for help While all the Hobbits I can think of have a combination of first- and lastname (e.g., Bilbo Baggins, Peregrin Took, the Sackville-Baggins's,...), I can't think of any character* of another race that has a lastname:   Men seem to like to add a reference to their ancestors (e.g., Aragorn, Arathorn's son or Isildur's heir) Dwarves seem to like descriptive or honorary names (e.g., Thorin Oakenshield, Dain Ironfoot). They are not lastnames though, since they do not get passed on to descendants. Elves don't have a need for lastnames, since elvish names are unique. Some nevertheless seem to have an additive (e.g., Legolas Greenleaf). Likewise, I can't find any usage of lastnames among Ents, Eagles, Istari, Orcs, trolls,...   But why would a society that is quite rural and not a leader of modernization be the only one to use a modern naming system with first- and lastnames?  *Except for Tom Bombandil. But he is, well, "special". $dx$ appears in differential equations, such us derivatives and integrals.  For example, a function $f(x)$ its first derivative is $\dfrac{d}{dx}f(x)$ and its integral $\displaystyle\int f(x)dx$. But I don't really understand what $dx$ is. A children's book series about a farm that grows massive food There was a series of illustrated children's books that I was introduced to as a child in the late 1980's early 1990's.  The main character was a farmer - I can't remember the name, but I think it was Mc or Mac something. He bought his farm from a sleazy character who was trying to cheat him. The farmland was originally some kind of swampy land, but this industrious character (and his family) discovered that the land would grow plants to a massive size - radishes the size of basketballs, etc.  There were some pretty fantastic stories and adventure that the character would get into, such as one winter the weather got so cold that the wind (not the air) outside froze. They went out and cut it up and stored it in the icebox and would thaw out some of the cold breeze later in the hot summer.  The sleazy character made a constant appearance, trying to swindle this family out of the farm.  My Google-Fu seems to fail me at every turn. Do you know what this series is? Footnotes in tables? I would like to have footnotes in tables, but the \footnote command does not work inside a table environment.  Googling one finds that this is , at least in the UK.  That link contains a list of solutions to the problem, but since the author of the FAQ does not believe that this is good style, no comparison is made between the different methods.  I am sure that there are good typographical reasons why in most situations it is undesirable to have footnotes in tables (although I have never come across them), however I have recently felt the need to do just this in a paper I am currently writing.  Therefore I'd like to ask two questions:   What are the arguments against footnotes in tables? If one really must go against the advice in 1., which method (whether considered in the  or not) would you recommend?   Thanks in advance.  Added  In response to ShreevatsaR's comment: I do not much care for where the text of the footnote appears.  I do however insist on the footnote marks being attached to the relevant entries in the table, so that I can avoid having to reference "the second entry in the eighth line of the table", etc... /usr/bin/sudo must be owned by uid 0 and have the setuid bit set I have run following command accidentally   sudo chown [username] -hR /   Now sudo su getting error:  sudo: /usr/bin/sudo must be owned by uid 0 and have the setuid bit set   How to Solve This? How to add a PPA on a server? The server version of Ubuntu does not have the  command. How can I add a  (PPA) to the server without this command? Arriving at a different port of entry in the same state in USA? I am a girl in my early twenties traveling to USA from India and in my visa application I have provided the contact address for a relative in San Francisco, and their invitation letter. I would like to visit LA first. Will I face problems during immigration if I land in LA (with an immediate on wards ticket to SF)? I dont plan to get on the flight from LA to SFO.  Initially I was planning to fly to SFO from India and then fly to LA immediately after completing immigration at SFO airport.