How to solve modular equivalence with polynomial I'm finding the solutions for the modular equation $x^2 -3x+2 \equiv 0\pmod{14}$. This is what I've done so far:  \begin{align} 0 &amp; \equiv x^2 -3x+2 \pmod{14}\\ &amp; \equiv (x-1)(x-2) \pmod{14} \\ \end{align} This implies that two of the solutions are the polynomial's usual roots: 1, 2.  This is where I get lost. I realize I should be using the following fact to find the other solutions, but don't know how to approach it.$$(x-1)(x-2) \overset{14}{\equiv} 0 \Leftrightarrow 14|(x-1)(x-2)$$ The provided answer says that 8,9 are the other solutions. How would I go about finding these?
Solve $x^2+5x+6 \equiv 0 \pmod{\!11\cdot 17}$ Solve $x^2+5x+6 \equiv 187 \mod 187$ Solution $$x^2+5x+6 \equiv 187 \mod 187$$ $$ (x+\frac{5}{2})^2 \equiv \frac{1}{4}$$ $$ 4(x+\frac{5}{2})^2 \equiv 1$$ $$ y:= x+\frac{5}{2} $$ $$ 4y^2 \equiv 1 \mod 11 \wedge 4y^2 \equiv 1 \mod 17  $$ $$ ( 2y \equiv 1 \mod 11 \vee 2y \equiv 10 \mod 11 ) \wedge ( 2y \equiv 1 \mod 17  \vee 2y \equiv 13 \mod 17)  $$ $$ ( y \equiv 6 \mod 11 \vee y \equiv 5 \mod 11 ) \wedge ( y \equiv 9 \mod 17  \vee y \equiv 15 \mod 17)  $$ Combining that from CRT I got: $$ y \in \left\{49, 60,83,94 \right\} $$ and for example: $$ x+\frac{5}{2}  \equiv 94 \mod 187$$ $$ 2x  \equiv 183 \mod 187$$ some calculus and get... $$x \equiv 185 $$ And the same thing for each other case. Question Is there any faster (or smarter) way to solve equations like that?
Why do we use "dried up" instead of just "dried"? The creek has dried up.   In this example sentence, you should say "dried up." If you say just "dried," it sounds incomplete. Is this an example of an idiom or is there a grammatical rule governing this instance? If so, what is it? Guarding against cryptanalytic breakthroughs: combining multiple hash functions I've never really got how chmod worked up until today. I followed a tutorial that explained a big deal to me.   For example, I've read that you've got three different permission groups:   owner (u) group (g) everyone (o)   Based on these three groups, I now know that:   If the file is owned by the user, the user permissions determine the access. If the group of the file is the same as the user's group, the group permission determine the access. If the user is not the file owner, and is not in the group, then the other permission is used.   I've also learned that you've got the following permissions:   read (r) write (w) execute (x)   I created a directory to test my newly acquired knowledge:  mkdir test   Then I did some tests:  chmod u+rwx test/ # drwx------ chmod g+rx test/ # drwxr-x--- chmod u-x test/ # drw-r-x---   After fooling around for some time I think I finally got the hang of chmod and the way you set permission using this command.    But...  I still have a few questions:   What does the d at the start stand for? What's the name and use of the containing slot and what other values can it hold? How can I set and unset it? What is the value for this d? (As you only have 7=4+2+1 7=4+2+1 7=4+2+1) Why do people sometimes use 0777 instead of 777 to set their permissions?   But as I shouldn't be asking multiple questions, I'll try to ask it in one question.  In UNIX based system such as all Linux distributions, concerning the permissions, what does the first part (d) stand for and what's the use for this part of the permissions? Install Ubuntu 12.10 instead of Windows 8 I was running my OS off a USB stick fine and the wifi was working. I installed it to my SSD and setup again but not the WIFI adaptor isn't working.  I followed the first time  and it worked but since installing onto the SSD and doing the same its not working.  No wlan0 interface found Please check drivers, try lsusb to check USB device is present root@goldminer:~# lsusb Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 002: ID 0bda:0811 Realtek Semiconductor Corp.  Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub   On the working device  root@coalminer:~# dkms status amdgpu, 18.10-572953, 4.13.16-hiveos, x86_64: installed amdgpu, 18.10-572953, 4.4.0-127-generic, x86_64: installed nvidia, 390.59, 4.13.16-hiveos, x86_64: installed nvidia, 390.59, 4.4.0-127-generic, x86_64: installed rtl8812au, 4.2.2, 4.13.16-hiveos, x86_64: installed rtl8812au, 4.2.2, 4.4.0-127-generic, x86_64: installed   On the SSD  root@goldminer:~# dkms status amdgpu, 18.10-572953, 4.13.16-hiveos, x86_64: installed amdgpu, 18.10-572953, 4.4.0-127-generic, x86_64: installed nvidia, 390.59, 4.13.16-hiveos, x86_64: installed nvidia, 390.59, 4.4.0-127-generic, x86_64: installed rtl8812au, 4.2.2, 4.13.16-hiveos, x86_64: installed (WARNING! Diff between built and installed module!) rtl8812au, 4.3.8.12175.20140902+dfsg: added rtl8812au, 5.2.9: added   Any advise? I think from trying to fix it ive been making it worse. My daughter applied at the Italian Consulate in Philadelphia, and they gave her two entries for 20 days (we thought it was for 20 days each entry). She was in Italy 12 days, then went to England for 1 week and flew to Venice to take a 10-day cruise. She couldn't make it because they said she has only 8 remaining days, but she still has a land tour already paid this week.  What can she do? Can she extend the Schengen visa for 12 more days? Right now, she is in Madrid, but next week she has to fly from Barcelona to Paris to start with the tour. What would happen if she decides to take the tour with the expired visa? She is a US permanent resident. Use of var keyword in C# I installed Linux Mint in 2 partitions: / and /home  Windows 8 is under UEFI boot mode.  How to hide those linux partitions in Explorer?    When I click on them: Not sure if there is a cultural difference. In our family it is considered normal to frighten the child so that he behaves the way we want.  Example- Parent: Eat that quickly or the God will punish you! Parent: Don't go on the stairs. The ghost is hiding there and it'll catch you! Parent: Be quiet or the police will grab you!  Does this kind of behavior from the parent's side has any abnormal effects on the baby in the longer run? Can this behavior be accepted as normal?  Has any research been done on this aspect? Disk full, du tells different. How to further investigate? I have a SCSI disk in a server (hardware Raid 1), 32G, ext3 filesytem. df tells me that the disk is 100% full. If I delete 1G this is correctly shown.  However, if I run a du -h -x / then du tells me that only 12G are used (I use -x because of some Samba mounts).  So my question is not about subtle differences between the du and df commands but about how I can find out what causes this huge difference?  I rebooted the machine for a fsck that went w/out errors. Should I run badblocks? lsof shows me no open deleted files, lost+found is empty and there is no obvious warn/err/fail statement in the messages file.  Feel free to ask for further details of the setup. Which textbook is good for introductory group theory? Okami is now reborn in High Definition for PS3. The graphics are obviously better, sharper and yet preserves the gist of the original game, however I can swear some of the texts have changed as well.  My PS2 console is no longer available to me so I can't test it myself, but does anyone know whether there are any changes to the game (aside from graphics) or not? How can I set default terminal used in Unity? How can I set the default terminal used in Unity?  I would like to use the Ctrl+Alt+T hotkey to start a non-default terminal. The default terminal is gnome-terminal.   Where can I change the default terminal value? Has the wall been repaired? Compute the integral $\int\frac{dx}{(x^2-x+1)\sqrt{x^2+x+1}}$ "1 out of 100 chickens is" or "1 out of 100 chickens are"? I'm in an argument. To me "are" makes more sense. I understand the rationale for is because it's only one chicken, but chickens itself is plural. Help? Is it possible to write any bounded continuous function as a uniform limit of smooth functions Is $C^\infty(\mathbb{R})\subset C_b(\mathbb{R})$ dense? I.e. is any continuous bounded function $f:\mathbb{R}\to\mathbb{R}$ the uniform limit of smooth functions?   On any bounded interval this is true since by Stone-Weierstrass polynomials are smooth and dense in the continuous functions. I guess the result is still true for $\mathbb{R}$ but I don't know how to prove it. Since I don't have any integrability conditions on $f$ the technique of convoluting with mollifiers is probably not applicable. Visa for transit in Seoul I think we need a button that says Edit and Close added to the Review Close button options.  Many of these closed posts will be around forever (and should be, closed should not just be a path to deletion), so they need editing.  If I edit it now it goes away, with the only option being a back click to get back to the review, and then click into the post and edit it.  We have an Edit and Reopen button, so this would fit in just fine. Why disable Fast Boot on Windows 8 when having dual booting? Why is everybody keep mentioning to disable Fast Boot on Windows 8 if you have installed alongside Ubuntu? Is it something that is recommended only for UEFI machines or is it a suggestion for Legacy BIOS machines as well? Is it because it makes the Windows partition inaccessible from Linux or there is another more serious reason to disable it?