Can someone please help me on this problem in modular Arithmetic Congruences I ran into this problem on aops alcumus If $3x+7\equiv 2\pmod{16}$, then $2x+11$ is congruent $\pmod{16}$ to what integer between $0$ and $15$, inclusive?
What is the best way to solve equations like the following:  $9x \equiv 33 \pmod{43}$  The only way I know would be to try all multiples of $43$ and $9$ and compare until I get $33$ for the remainder.  Is there a more efficient way ?   Help would be greatly appreciated!
pgrouting unexpected output What is a general rule for use of auxiliary verbs in sentence? Should we duplicate it or not? For instance,     It is available for every item and (is) used with . . . I can't see my background image in the 3D view I try to set up an image as background for a basic blender tutorial, but it isn't visible.  This is the image I try to have as background: What is the max variance distribution with fixed mean and support Is there a upper bound on the variance for a distribution that is confined say, in $[0,1]$, and has fixed mean $\mu \in [0, 1]$ How do I Uninstall Windows 10 or Windows 10 preview? Can't view deleted questions via Android app I want to talk to someone about the house that my wife and I own.  Saying, for example, "My wife's and my house is awesome," sounds a bit funny to me.  What's the best way to express this?  Clarification  I'm asking specifically about the grammar of multiple nouns in possessive form.  I'm particularly curious if it's possible to do this with a first-person pronoun (me).  I am capable of rephrasing this in other ways - my question is not how to express the idea, but about this particular grammatical construction, if it is even legal. It is a theorem in elementary number theory that if $p$ is a prime and congruent to 1 mod 4, then it is the sum of two squares. Apparently there is a trick involving arithmetic in the gaussian integers that lets you prove this quickly. Can anyone explain it? Convert ls -l output format to chmod format How would I go about creating a 3D MMORPG Mouse Look? How would I go about creating a 3D MMORPG Mouse Look? I have created a 3D Space Rpg that is almost finished with success so far. However, I didn't have a clue, how I would attempt to make a Mouse Look method where if a user right clickes and then holds the right mouse button and moves it around the camera moves around with the mouse. The camera can not move away from your character/ship, it should act as if the character/ship is it's origin and that it rotates all around the origin.  I don't mind coding this with python either. Advice is welcome! In the example  $\cup^{i=1}_{\infty}F_i$   How do you get the i=1 directly below the union symbol and the infinity directly above? If I have an object implementing the Map interface in Java and I wish to iterate over every pair contained within it,  what is the most efficient way of going through the map?  Will the ordering of elements depend on the specific map implementation that I have for the interface? If you visit a chat room attached to a beta site while logged out, the log in message is all but unreadable, being dark grey on a dark blue background. For example, visit  while logged out or in private browsing mode. I want to see you.   I look forward to seeing you.      How can one say "to" in the first sentence is an infinitive marker and in the second sentence a preposition when we are given just the following two sentences and are asked to fill in the blanks?        I want to ____(see/seeing) you.   I look forward to __(see/seeing) you. No internet after 16.04 LTS 18.04.01 upgrade This may seem like a duplicate, but many solutions have been unsuccessfully tried. Currently I have no internet, WIFI or Ethernet. Sometimes: "no wifi adapter found".  The device is HP dm4, dual boot with Windows 7.    Here is the  The issue started 3 weeks ago as no GUI after 16.04 LTS to 18.04.01 upgrade.  At that time, I was able to use the terminal to connect to the Internet and run "fixes" in   Then mysteriously, the GUI ran after restarting several times.  But since then, I am unable to connect to the Internet in the terminal or GUI.    There is a chatroom  about my issues.  sudo nmcli c up &lt;saved WIFI connection&gt;   only appears to connect.   sudo nmcli d wifi list   shows strong signal strength, but ping to google and nyt fails.   The phone I use as a hotspot shows a successful connection.    In the GUI Network Tools show the phone/hotspot recently used minutes ago, the Available Networks list shows the phone/hotspot as available with a check mark, but the "connect" button is grayed out and unfunctional.    REGDOMAIN=00 and attempts to change this has failed as others describe. I have a similar set up to the one described by cipricus in  and the situation described in how many distinct values does it have? BASH script to set environment variables not working I've written the following script to set some environment variables when needed.  #!/bin/sh export BASE=/home/develop/trees echo $BASE export PATH=$PATH:$BASE echo $PATH   Below the command and the results I can see on my terminal: the script runs, but the variables are not set at the end.  ~$: ./script.sh /home/develop/trees /bin:......:/home/develop/trees ~$: echo $BASE  ~$:    What's wrong? Thanks in advance. Mirko Split Excel table over multiple PowerPoint slides I have a table in Excel which is too long for one PowerPoint slide. So I would like to split it over 2 or 3 slides, but have the header on each of the slides. What is the easiest way to accomplish that? I am using Excel and PowerPoint 2007. Is there a rule of thumb for objective questions asked out of curiosity? Karn, the Great Creator - what defines a 'card from outside the game' in sealed? In the upcoming set 'War of the Spark' there is the Planeswalker . His -2 ability reads as:      -2: You may choose an artifact card you own from outside the game or in exile, reveal that card and add it to your hand    Now my question is, in a sealed tournament, like the Prerelease, is a player allowed to also choose cards from outside his sealed cardpool, or only out of the cards therein. Does anyone know any rulings on stuff like that?