Proof of unit digit of $a^2$ Using Modular arithmetic.
Divisibility by 7 rule, and Congruence Arithmetic Laws
MySQL: "UPDATE command denied to user ''@'localhost'" On the old style user pages such as mathoverflow I noticed that the long comment on the right is floating lower today than it did previously (as recently as yesterday). I don't know if we care, but I noticed it. Getting Acquaintances to become Friends Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.   I thought I would do the following ... As $n$ is not divisible by $2$ and $3$ then $$n=2k+1\;\text{or}\\n=3k+1\;\text{or}\\n=3k+2\;\;\;\;$$for some $n\in\mathbb{N}$. And then make induction over $k$ in each case.$$24\mid (2k+1)^2-1\;\text{or}\\24\mid (3k+1)^2-1\;\text{or}\\24\mid (3k+2)^2-1\;\;\;\;$$This question is in a text of Euclidean Division I'm reviewing, and I wonder if there is a simpler, faster, or direct this way. How do I configure internet connection for Terminal on Ubuntu 14.04? I've installed on Ubuntu 14.04 and with I've Broadband connection setup, Browser connection is OK,  but Terminal not connection via internet, when command type "sudo apt-get update" by terminal then showing me Error, see screenshot, How I can fix this ? Tips to extend battery life for laptops and notebooks What point (pt) font size are \Large etc.? In the preamble I have:  \documentclass[a4paper,11pt]{article} \usepackage{fontspec} \setmainfont{Arial}   What can be inferred about the real font pt size for the following?  \tiny, \scriptsize, \footnotesize, \small, \normalsize, \large, \Large, \LARGE, \huge, \Huge How is the Schroedinger equation a wave equation? Wave equations take the form:  $$\frac{ \partial^2 f}  {\partial t^2} = c^2 \nabla ^2f$$  But the Schroedinger equation takes the form:  $$i \hbar \frac{ \partial f}  {\partial t} = - \frac{\hbar ^2}{2m}\nabla ^2f + U(x) f$$  The partials with respect to time are not the same order. How can Schroedinger's equation be regarded as a wave equation?  And why are interference patterns (e.g in the double-slit experiment) so similar for water waves and quantum wavefunctions? How to turn off Facebook notifications on Mac OS X? How to turn off Facebook notifications on Mac OS X Mountain Lion? Which singular names ending in “s” form possessives with only a bare apostrophe? Many questions already ask about this topic ( , , etc.) and their answers vary, but they always give exceptions to the apostrophe-s rule, for example:      6.24 The general rule for the possessive of nouns covers most proper nouns, including most names ending in sibilants."   Examples they give include Kansas’s, Ross’s land, and Jones’s reputation. Exceptions include Jesus’  and Moses’.  Which names does this apply to?  Is the Aeneas’  form correct, or is it Aeneas’s instead? How to Link/Append a data-block using the Python API? I'm searching a way to append a group in Python.  It should behave exactly like the Append function (ShiftF1) works, all objects should be local and editable. The idea is to append a character (with rig etc.) via Python and not Link it (to be able to modify it without making everything local one by one).  Thanks Modern ice-age/plans for weapon hidden in genome I am tired of always trying to guess, if I should escape special characters like '()[]{}|' etc. when using many implementations of regexps.  It is different with, for example, Python, sed, grep, awk, Perl, rename, Apache, find and so on. Is there any rule set which tells when I should, and when I should not, escape special characters? Does it depend on the regexp type, like PCRE, POSIX or extended regexps? Will my Chinese visa still be valid if I renew my passport? If so how does that work?  I have heard that you can travel with your new passport and just show the old passport with the valid visa when entering China. Has anyone done that? Recently?   I have also been told that you have to get a new visa, which seems somewhat logical but frustrating, especially when my Chinese visa is only a few months old.  My Chinese visa was issued in late Nov 2014 and I heard the rules changed between the US and China. My visa says it's good for 10 years and my US passport expires in 5. limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$ Show that $$\sup_{x\in [a,b]} f(x) = \lim_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$$ for f continuous and positive on [a,b].  I can show that LHS is greater than or equal to RHS but I can't show the other direction. What are character special and block special files in a unix system? How can I prevent 'grep' from showing up in ps results? When I  search for some process that doesn't exist, e.g.  $ ps aux | grep fnord                           wayne    15745  0.0  0.0  13580   928 pts/6    S+   03:58   0:00 grep fnord   Obviously I don't care about grep - that makes as much sense as searching for the ps process!  How can I prevent grep from showing up in the results? How do you prove the second law of thermodynamics from statistical mechanics? Do you say "I like apple" or "I like apples"? When stating a general fact/preference on countable nouns, singular or plural is more suitable and natural? Example 1 :  I like apple. or I like apples.  Example 2:  I like eating apple. or I like eating apples. How to completely remove desktop? I wanted to switch to Xfce (I had KDE and GNOME installed), and I did this :    sudo apt-get install xubuntu-desktop sudo apt-get remove kubuntu-desktop sudo apt-get remove ubuntu-desktop sudo apt-get autoremove   but to my surprise, I could still pick gnome, kde plasma, etc during the log in.  So, how do I completely remove KDE and GNOME desktops?