$7^{21}\cdot 2^{50}+a$ is divisible by $9$
Mod of numbers with large exponents [modular order reduction]
Why is my find not recursive? I am running the following command, but it is not performed recursively:  find . -name *.java   I know there are java files further down in the current directory but it is performing the find on the current directory only. I am using OS X, 10.9. $2\times2$ matrix $A$ such that $A$ has one independent eigenvector while $A^{2}$ has two independent eigenvectors PHP & MYSQL: using group by for categories What is the difference between "speaking" and "talking"? It seems more politically correct to say that someone is speaking rather than talking.  What is the definitive difference between these terms? Should there be a comma in 'a 30-day, money-back guarantee'? Windows 7 Taskbar Icon Highlight Sticks After running Win 7 for some unknown period of time, the taskbar icon highlight starts to stick (video demo here: ). If I restart or kill explorer.exe and relaunch, it goes away.  Any idea what might be causing this? Yesterday I was filming a scene with my phone but suddenly the application crashed and when I try to open the m4v generated it says that is corrupted.  I have downloaded the video files (around 36MB) on my PC and I am trying to open and repair it. Can you suggest me a way to do it?  FFMPEG info  As suggested in comments I try check what FFMPEG says me about that file with this command  ffmpeg.exe -i VID_20120425_144739.m4v -c:v copy -c:a copy out.mp4 2&gt; log.txt   Here it is the result:  ffmpeg version N-40126-ga4b58fd Copyright (c) 2000-2012 the FFmpeg developers   built on Apr 26 2012 03:29:50 with gcc 4.6.3   configuration: --enable-gpl --enable-version3 --disable-w32threads --enable-runtime-cpudetect --enable-avisynth --enable-bzlib --enable-frei0r --enable-libass --enable-libcelt --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libfreetype --enable-libgsm --enable-libmp3lame --enable-libnut --enable-libopenjpeg --enable-librtmp --enable-libschroedinger --enable-libspeex --enable-libtheora --enable-libutvideo --enable-libvo-aacenc --enable-libvo-amrwbenc --enable-libvorbis --enable-libvpx --enable-libx264 --enable-libxavs --enable-libxvid --enable-zlib   libavutil      51. 47.100 / 51. 47.100   libavcodec     54. 15.100 / 54. 15.100   libavformat    54.  3.100 / 54.  3.100   libavdevice    53.  4.100 / 53.  4.100   libavfilter     2. 72.100 /  2. 72.100   libswscale      2.  1.100 /  2.  1.100   libswresample   0. 11.100 /  0. 11.100   libpostproc    52.  0.100 / 52.  0.100 [mov,mp4,m4a,3gp,3g2,mj2 @ 003fc940] moov atom not found VID_20120425_144739.m4v: Invalid data found when processing input   Latest two lines are displayed in red. Can Superman see through his eyelids? Given that his x-ray vision allows him to see though skin, can he use this ability with his eyes closed? Or do they prevent it somehow? I understand that \bf and \it are now obsolete in LaTeX and that \textbf and \textit are proper, as they produce more sophisticated (in particular, cumulative and properly kerned) changes to font style. I have read the  and I understand the rules and their reasons, as well as the several other commands that are affected.  However, I find it convenient to use LaTeX for notetaking during lectures, and in that rushed environment, shortening a command by any number of keystrokes helps keep me from falling behind. \bf and its two-letter kin are still very useful to me for that reason, and once a presentation is finished I can go through and replace all appearances of \bf et al. with \textbf et al.  My question is this: is there a plan eventually to replace the short font style commands like \bf with the implementations of \textbf etc. some day, or should I expect \bf always to remain in existence but obsolete, for reasons of backward compatibility with original TeX? Original TeX has been greatly improved on in countless ways, but in the heat of transcription I sometimes miss its conciseness. How to overwrite an excel application without prompting the users Meaning of syntax $N(\mathbf{y} \mid \mathbf{0}, \mathbf{K})$ (multivariate normal distribution) In fact, of these, only Charcoal shows a recent time stamp. ArcGIS Python Tool - Importing Custom Script Into ToolValidator Class How did Thanos know about the power of "The Snap"? In the scene on Titan with Doctor Strange in Avengers: Infinity War, Thanos said,     With all six Infinity Stones, I will simply snap my fingers and it would all cease to exist.   Then again, in the very first scene with Thor and Loki, when Maw gave Thanos the Space Stone, he said that no one has ever worn two Infinity Stones together.   So how come Thanos knew about the power of the Snap? Because as Wong puts it to Tony, the Big Bang hurled the six Infinity Stones across the universe.   So if no one had collected all the six stones before Thanos, then how did he know about the ability to "Snap"? Assume that $f(x),g(x)$ are positive and are in $L^1$. Moreover, they are differentiable and their derivative is integrable. Let $h(x)=f(x)*g(x)$, the convolution of $f$ and $g$. Does the derivative of $h(x)$ exist? If yes, how can we prove that $$ \frac{d}{dx}(f(x)*g(x)) = \left(\frac{d}{dx}f(x)\right)*g(x)$$  Thanks Pretty printing XML with javascript Reduce minimum in call volume I find that the minimum in-call volume on my HTC Desire is still far to loud on some calls.  Since I got the phone, I have flashed several different custom ROMs, radio updates, etc, and have had the issue throughout.  Do you know of any way (setting, hack, app, whatever) to reduce the minimum volume?  My device is rooted and I am currently running one of the CyanogenMod 7 (Gingerbread) nightly builds. Can I re-create deleted Gmail accounts? A long time ago, I created a Google mail account. I fell for a trap that was common back then (not sure how it is nowadays) and ended up with two Google accounts—one for Gmail (using the Gmail email address I would like to use) and one for everything else (using an email address at an external mail provider).  Hoping that I could associate my Gmail and my actual Google account, I deleted my Gmail account only to discover that deleted account names cannot be used again. So basically my old Gmail account along with the Google email address I would like to use is gone.  My main Google account got assigned a different Gmail account in the mean time.  Do you know if it is possible to re-use my preferred Gmail address? If possible, I would like to assign it to my main Google account. But I'd also be happy to have it as a second Google account, anything is better than the current situation. How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$ How to get autofocus to work with D5100 and AF-P DX Nikkor I just bought Nikon 18 - 55 mm f/3.5 - 5.6G VR AF-P DX Nikkor from .  When I connected it to my Nikon D5100, the autofocus didn't work. There was nothing about this from the original seller's website.  Is there anything I can do short of returning?