$2^b-1$ does not divide $2^a+1$,how can I show it? $$\text{ If } a,b \geq 3, \text{ show that } \  2^b-1 \text{ does not divide } 2^a+1$$  How can I do this? Could you give me a hint?
Prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$ I'm trying to prove $2^b-1$ does not divide $2^a + 1$ for $a,b&gt;2$. Can someone give a hint in the right direction for this?
"that which" used together When I read essays from Eliot, I find him using "that which" frequently, e.g.        the combination which is the murder of Agamemnon is probably as complex as that which is the voyage of Ulysses.   A very small part of acting is that which takes place on the stage!   They belong to a different race. Their crudity is that which was of the Roman, as compared with the Greek, in real life.      I can kind of guess its usage, but I want to know more about this grammar structure. Searching on Google mostly gave me the simple difference between "that" and "which", and some examples using "that which":        that which we call a rose (from "Romeo and Juliet")   that which we persist in doing      It is a pity that Google search does not direct me to any useful page about "that which".  Can someone explicate its grammar for me? Cantor's diagonal argument can be used to show that a set $S$ is always smaller than its power set $\wp(S)$.  The proof works by showing that no function $f : S \rightarrow \wp(S)$ can be surjective by constructing the explicit set $D = \{ x \in S | x \notin f(s) \}$ from a function $f$ and showing that no element of $S$ maps to $D$.  This proof works because all bijections are surjections, so if no surjection from $S$ to $\wp(S)$ exists, then there cannot be a bijection between $S$ and $\wp(S)$.  My question is whether it is possible to run a "reverse diagonalization" that works by instead showing that there is no injection from $\wp(S)$ to $S$.  I am curious about this because I have never seen Cantor's theorem proved this way (or, more generally, any diagonal argument structured like this).  Is it possible to take Cantor's diagonal argument and "reverse" it to show that there cannot be an injection from $\wp(S)$ to $S$, rather than showing that there can be no surjection from $S$ to $\wp(S)$?  Thanks! Feed can show entries for deleted posts, which viewing them fails How to add a script to Startup Applications from the command line? Where, precisely, does feedback on Community ♦ generated flags go to die? For the most part, I treat "Community" like any other user when handling system raised flags. If they are useful, I mark them as such. If they are noise, I dismiss them as such. The Community user has a static flag weight, so our reaction to them is more or less feedback for developers.  Is this feedback from moderators network wide used in any way to help improve the accuracy of system raised flags? Or, would clicking either button suffice?  I'm asking because our reasoning behind declining a flag is now more precise. Does dismissing some as noise help improve the criteria that ultimately generates the flag?  Edit  Yes, thank you Skype, I realize that  asked a similar question . Change Text Color in Blender Game Engine? I want to change the color of some text in my game. I've tried adding materials, but whenever I press P to play the game, the text stays the same white color. Any ideas? Can an Indian citizen holding a valid USA visa visit Colombia without a visa? I am planning to travel to Colombia for about a week to attend an academic conference. I am an Indian passport holder currently living in USA with a F-1 visa. Do I need to obtain a visa beforehand from the Colombian consulate?  I have found   that claim that Indian citizens holding a valid USA visa are not required to apply for Colombian visa.     However, I am not sure if these sources are "official" and trustworthy.Is there a more official source? Also, does this rule apply to "tourists" only? Does anyone have any personal experience with this rule? How do I unit test (using xUnit) a class that has internal private methods, fields or nested classes? Or a function that is made private by having  (static in C/C++) or is in a private () namespace?  It seems bad to change the access modifier for a method or function just to be able to run a test. No package php-imap available on CentOS 7 I'm running a dedicated server with CentOS 7 64bit, here is the output when trying to install IMAP:    yum install php-imap   Loaded plugins: fastestmirror   Loading mirror speeds from cached hostfile    * base: ftp.ciril.fr    * extras: ftp.ciril.fr    * updates: ftp.ciril.fr   No package php-imap available.   Error: Nothing to do       Also the same when disabling exclusions:    sudo yum install --disableexcludes=all php-imap Loaded plugins: fastestmirror Loading mirror speeds from cached hostfile  * base: ftp.ciril.fr  * extras: ftp.ciril.fr  * updates: ftp.ciril.fr No package php-imap available. Error: Nothing to do Does the series $\sum_{n=1}^{\infty}|x|^\sqrt n$ converge pointwise? If it then what would be the sum? Does the series $\sum_{n=1}^{\infty}|x|^\sqrt n$ converge pointwise? This is a question you can read everywhere on the web with various answers:  $ext = end(explode('.', $filename)); $ext = substr(strrchr($filename, '.'), 1); $ext = substr($filename, strrpos($filename, '.') + 1); $ext = preg_replace('/^.*\.([^.]+)$/D', '$1', $filename);  $exts = split("[/\\.]", $filename); $n    = count($exts)-1; $ext  = $exts[$n];   etc.  However, there is always "the best way" and it should be on Stack Overflow. Bugged display in search using negation If two coins are flipped and one gets head, what is the probability that both get head? There is this puzzling thing that is called : paradoxically, warm (35°C) water freezes faster than cold (5°C) water.  As a physisist, I've been asked about it several times already. And I have no definite answer to that, apart from the standard: "there are many things that can influence it".  So, does anyone knows about the status or progress on that effect? Any recent reviews, publications or other references? How to create a rounded cone How do I find out which process is eating up my bandwidth? I think I'm being the victim of a bug here. Sometimes while I'm working (I still don't know why), my network traffic goes up to 200 KB/s and stays that way, even tough I'm not doing anything internet-related.   This sometimes happens to me with the CPU usage. When it does, I just run a top command to find out which process is responsible and then kill it. Problem is: I have no way of knowing which process is responsible for my high network usage. Both the resource monitor and the top command only tell me my total network usage, neither of them tells me process specific network info.  I've found questions here about monitoring total bandwidth usage, but, as I mentioned, that's not what I need. Is there another command I can use to find out which process is getting out of hand?  The command iftop gives results that disagree entirely with the information reported by System Monitor. While the latter claims there's high network traffic, the former claims there's barely 1 KB/s.  I've already tried killing all the obvious ones (Firefox, update-manager, Pidgin, etc) with no luck. So far, restarting the machine is the only way I found of getting rid of the issue. How do I access a specific element in a vector of vectors clojure What open source software for auto-alignment of photographs? Do you know any open source tool to automatically align images, similar to the auto align feature in Photoshop? Why is the sum of the digits in a multiple of 9 also a multiple of 9? The sum of the digits in $9 k$ (where $k$ is an integer) is a multiple of $9$: for example   $$9\cdot 1=9$$ $$9\cdot 7=63 \qquad  \text{and } 6+3=9\cdot 1$$ $$9\cdot 11=99 \qquad \text{and }  9+9=9\cdot 2$$  But why? Prove or disprove an inequality involving complex numbers Consider following inequality:     $|z_1 + z_2|\ge|z_1| - |z_2|  \  \ \ \ \ \  z_1,z_2 \in \mathbb{C}$   Is that true always? I tried many examples and it was correct but I don't know how to prove that if it's right.