Find all solutions to the diophantine  equation $7^x=3^y+4$ in positive integers. I couldn't have much progress.  Clearly $(x,y)=(1,1)$ is a solution. And there's no solution for $y=2$. Assume $y \ge 3$ and $x \ge 1$. By $\mod 9$, we get $7^x \equiv 4\mod 9 \implies x \equiv 2 \mod 3 $. By $\mod 7$,we get $y \equiv 1 \mod 6$. I also tried $\mod 2$ but it didn't work. Please post hints ( not a solution). Thanks in advance!
I don't know how to solve $7^x-3^y=4$... I tried to see something $\pmod 7$ and $\pmod 3$ but it doesn't help at all. Can anyone give me some hints about it?
What is *.pkinfo file? What is a *.pkinfo file?   Google Search results talk about Package Info files and how they contain map documents and layers, so I don't see how this is different from a .mpk file.    I also have not found anything about how to create a *.pkinfo file. $\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$ While using MathJax to typeset binomial coefficients, I came across this problem of different sized brackets if my lower index contains the '0' character. Is there anyway to make the brackets the same size? Multiple Installations and Understanding $PATH I have an older version of Git installed at:  /usr/bin/   I recently downloaded a newer version to:  /usr/local/bin   When I type:  which git   I get the location of the old version. I believe that this is just because /usr/bin/ appears before /usr/local/bin in my $PATH variable and so the older version of git is 'found' first.   To test this, I renamed the older version of git to "git_old". Now when I type:  which git   I get the location of the newer version, as expected. But when I type:  git --version   I get the following error:  -bash: /usr/bin/git: No such file or directory   I'm just wondering why my computer is going back to looking in the old location for Git? Unable to disable Hyper-V in Windows 10 Hi I installed Docker for Windows which enabled Hyper-V on my windows 10 machine. Unfortunately this caused Virtual Box to not work anymore, therefore I removed Docker again, but Hyper-V is still activated.  If I try to disable Hyper-V with any of those ways:  on the reboot it will first try to apply the changes and than say that the changes couldn't be applied and reverts, so Hyper-V is activated again.  Has anybody an idea what could be the issue here? Returning an unevaluated expression with values substituted in Before you disagree with me with a downvote, or just want to be funny, please hear me out. From the :  The upvote privilege comes first because that's what you should focus on: pushing great content to the top. Downvoting should be reserved for extreme cases. It's not meant as a substitute for communication and editing.  I have honestly never seen a downvote reserved for an extreme case. The process is usually 1) downvote post if it's bad and don't comment. (Not much of a process, is it?) As you stay on the site longer and longer, you develop a carelessness towards downvotes (as I have), but for new users, it's really discouraging.  question inspired me to [ask balpha to] make , which is a list of users with 1 rep who have the  badge. That's the closest I could get to new users who deleted their own posts after downvotes came in. Don't get me wrong, I know the argument about being nice to new users very well, but I still believe it to be an issue. And since , users are much more inclined to go the lazy route and downvote bad questions. No alternative measures (see below) are taken, for the most part. Personally, I leave a comment and don't downvote until the asker shows no interest in fixing their post. The only other measure taken to discourage downvotes (on answers) is the -1 rep punishment to the downvoter, which is absolutely meaningless and inconsequential anyways. How are we supposed to educate new users when we don't teach them what to do, don't direct them to the FAQ, and discourage them with downvotes right off the bat?  Instead of voting down: If the post is spammy or offensive — flag it. If the question is duplicate or off-topic — flag it for moderator attention. If something is wrong, please leave a comment or edit the post to correct it.  We claim to discourage downvoting, yet I see answers like  that encourage us to downvote first and ask questions later when a question is simply unclear or effortless. It's just an awful chain reaction. A new user comes to the site asking a question, but that doesn't work out too well, so they get downvotes, delete the question in shame, and don't get the help they deserve as a fellow writer of code and programmer. Strip away the quality of the site for a moment: the core functionality of this site, and the only reason I and a lot of other users are (still) on it, is to receive and give help to/from others. I enjoy making sure fellow programmers get the answer they need, because this site has helped me get mine when I needed them. Quality can still be maintained if content is fixed rather than downvoted more often. So can we stop discouraging new users from continuing to use this site and actually start to discourage downvoting? I think we need to encourage effort towards teaching and helping new users understand the system and why their post is bad rather than slapping them in the face with downvotes that they don't know how to interpret anyways. I'm leaving ways we can do this up to others. My first thought was to increase the punishment for downvoting answers and to no longer make question downvotes free, but those wouldn't be well-received, judging by the history of similar suggestions. . Symmetric and exterior power of representation Does there exist some simple formulas for the characters $$\chi_{\Lambda^{k}V}~~~~\text{and}~~~\chi_{\text{Sym}^{k}V},$$ where $V$ is a representation of some finite group?  Thanks. Solve the recurrence relation:$ T(n) = \sqrt{n} T \left(\sqrt n \right) + n$ Make all new files in a directory accessible to a group Suppose I have two users Alice and Bob and a group GROUPNAME and a folder foo, both users are members of GROUPNAME (using Linux and ext3).   If I save as user Alice a file under foo, the permissions are: -rw-r--r-- Alice Alice. However, is it possible to achieve that every file saved under some subdirectory of foo has permissions -rwxrwx--- Alice GROUPNAME (i.e. owner Alice, group GROUPNAME)? How to use JACK and Pulseaudio/ALSA at the same time on the same audio device? Whenever I launch hydrogen it breaks my audio in all other applications which use Pulse, for example, I can no longer play videos in Chrome after having launched Hydrogen once, until I restart my PC or do sudo alsa force-reload. I have found people with similar issues, but no actual guide to fix this, often there are links to  (which has moved to  ) I am using Ubuntu Studio 14.04 64bit.  ALTERNATIVELY if this is truly impossible to achieve, can someone tell me how to use Jack on one soundcard and Pulse on another? This way I could plug in a USB sound card only when I need JACK.  Please don't make me use windows. Data from multiple lists using single REST API call Emulate "double" using 2 "float"s Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$? I started with the hypotheses $(p \implies q) \implies p$ and $\sim p$. However, from these hypotheses I did not get the desired contradiction to solve the question.  Thanks sb45 Can one executable be both a console and GUI application? I want to make a  program that can be run as a CLI or GUI application depending on what flags are passed into it. Can this be done?  I have found these related questions, but they don't exactly cover my situation: proper use google webmaster tools URL Parameters There are some urls like http://domain.com/user/:username and http://domain.com/post/:id on my website, the username and id is the parameter from database. I try to let google crawler more efficiently , can I use google webmaster tools &gt; URL Parameters &gt; add parameter ? I read the document but still don't get it how to set up? the column Parameter and the rest what should I filled? or this tools only for get method parameter? What does the "yield" keyword do? What is the use of the yield keyword in Python? What does it do? For example, I'm trying to understand this code1: def _get_child_candidates(self, distance, min_dist, max_dist):     if self._leftchild and distance - max_dist &lt; self._median:         yield self._leftchild     if self._rightchild and distance + max_dist &gt;= self._median:         yield self._rightchild    And this is the caller: result, candidates = [], [self] while candidates:     node = candidates.pop()     distance = node._get_dist(obj)     if distance &lt;= max_dist and distance &gt;= min_dist:         result.extend(node._values)     candidates.extend(node._get_child_candidates(distance, min_dist, max_dist)) return result  What happens when the method _get_child_candidates is called? Is a list returned? A single element? Is it called again? When will subsequent calls stop?   1. This piece of code was written by Jochen Schulz (jrschulz), who made a great Python library for metric spaces. This is the link to the complete source: [Module mspace][1]. Radeon error atombios stuck in loop The screen goes blank and shows logs me out immediately a while after using multiple monitors.   dmesg shows:  [33786.908877] [drm:atom_op_jump [radeon]] *ERROR* atombios stuck in loop for more than 5secs aborting [33786.908901] [drm:atom_execute_table_locked [radeon]] *ERROR* atombios stuck executing 6DD2 (len 254, WS 0, PS 4) @ 0x6DE0 [33786.908910] [drm:atom_execute_table_locked [radeon]] *ERROR* atombios stuck executing 673E (len 78, WS 12, PS 8) @ 0x6777   lspci | grep -E 'VGA|Display' shows:  00:02.0 VGA compatible controller: Intel Corporation HD Graphics 5500 (rev 09) 03:00.0 Display controller: Advanced Micro Devices, Inc. [AMD/ATI] Sun  XT [Radeon HD 8670A/8670M/8690M / R5 M330 / M430] (rev 83)    explains exactly my situation. But I don't have /etc/modprobe.d/radeon.conf file. Suggested improvements to badges index page ()  Currently,  shows the possible badges, number of total recipients, and brief descriptions. However, I have a few suggestions (mostly minor changes) that could make it a bit nicer.   There is no way to see (on that page) which badges I've earned multiple times — they all appear with a green checkmark. It would be nice to show something like "x 4" like in the badges section of the user profile page. For example:      There is no way to see which badges can be awarded multiple times — you have to click on a specific badge to see yea or nay. It would be nice to have a small, simple icon next to badges that can be earned multiple times, similar to the checkmark showing which badges I've earned. The layout would be nicer if the number of recipients for each badge were in a separate column — since the badge images are different sizes, the overlap and ragged right alignment makes the numbers harder to read. An alternative view that groups badges by "achievement level" (gold/silver/bronze) would be nice, as would a view that groups progressive degrees of the same accomplishment. (e.g. Nice Answer &rarr; Good Answer &rarr; Great Answer OR Popular Question &rarr; Notable Question &rarr; Famous Question) Why can't pdflatex print EPS figures?