Fibonacci Cyclic Pattern
Is it true that the Fibonacci sequence has the remainders when divided by 3 repeating?
Are there critical hits for spells? How to tell if a set of vectors spans a space? I want to know if the set $\{(1, 1, 1), (3, 2, 1), (1, 1, 0), (1, 0, 0)\}$ spans $\mathbb{R}^3$. I know that if it spans $\mathbb{R}^3$, then for any $x, y, z, \in \mathbb{R}$, there exist $c_1, c_2, c_3, c_4$ such that $(x, y, z) = c_1(1, 1, 1) + c_2(3, 2, 1) + c_3(1, 1, 0) + c_4(1, 0, 0)$.  I've looked around the internet, but all the answers I found involve setting up a matrix and finding the determinant, and I can't do that here because my matrix isn't square. What am I missing here? My advisor wants me to include a name of someone who has no contribution to the paper My first advisor wants me to include my second advisor's name in a paper that I worked on before she (2nd advisor) came along.   Should I include her name even though she didn't do anything in that paper? I don't think she even read it. In MySql's interpreter, it's very easy to dump a table to the screen along with its field names.   There seems to be no simple way to export a table to a tab-delimted or CSV outfile including its column headers.  I'm trying to do this using only SQL or the Linux command line, without writing a program in another language.  Thank you How to retrieve multiple rows from database in PHP This is almost surely an Arzela-Ascoli question, since it comes from an old exam of which such problems are quite common. Unfortunately, I can't seem to get it though.  $\{ f_n \}$ is a sequence of functions $[0,1] \to \mathbb{R}$ satisfying $|f_n'(x)| \leq \frac{1 + |\ln (x)|}{\sqrt{x}}$ and $-10 \leq \int_0^1 f_n(x) dx \leq 10$ for every $n$. The question is to show the existence of a uniformly convergent subsequence.  In these kinds of situations, the bounds given usually turn into something nice  to force uniform boundedness. Maybe I could hope to establish equicontinuity using the integral somehow, but I'm not told that the $f_n$ are always positive, so the absolute values would probably screw things up anyway.  Is it an easy problem I'm missing or is this totally the wrong track? If so, what's the right track? I'm pretty sure the answer to this should be obvious - even to me ...  It's been a while I've been reading and attempting to construct simple electronic circuits. The supply almost always is either through a battery/cell, or AC duly rectified to DC.   I have the impression electronic circuits rarely ever work off an AC supply.    Is this impression correct? If yes, why is an electronic circuit rarely (if ever) powered/biased using straight AC? Replace \input{fileX} by the content of fileX automatically Suppose I have a document with multiple include or input statements  \input{fileA} \input{fileB}   etc.   Is there an easy way to generate a single .tex file where \input{fileA} is replaced by the actual content of fileA etc. without copying it manually? How can I access the apache basic-auth username in a PHP script? Why is CBS.log file size 20 GB In the Iron Man movie Tony flies the Iron Man armour from Miami to Afghanistan, roughly 7800 miles.    What is the maximum range of the Iron Man armour?   What sort of speed does the armour cruise at?  How long would the flight from Miami to Afghanistan have taken?   Could Iron Man circumnavigate the globe without stopping, and how long might this journey take him?   EDIT: Just found this (funny) image, New York to Washington in under an hour?!? :) On Windows 7 can one make UAC on an admin account prompt for the password, just like a limited account? I am one of the very few who likes the security of UAC and so I have the UAC set to "Always Notify" on my Admin account. But I would be even happier if the system would prompt me for a password, when notifying me.  I can get what I want by adding a second non-admin user and using that account.  But somehow it seems wasteful to have two accounts set up when I will always use the non-admin account day-to-day.  So I am wondering if there is any setting that would cause an Admin account to behave password-prompting-wise as a standard account? Compute the radius of convergence of the power series $\sum_{n=0}^{\infty} n!x^n$ I don't quite understand the difference between /a/ and /æ/. Google gives the transcription for 'add' as /ad/, while Wiktionary returns /æd/.  Are these sounds actually distinct or is this just two different ways of writing the same one? No more updates for Google Chrome 32-bit Finding a ray that intersects a polygon as many times as possible Why are the United States often referred to as America? python: restarting a loop UIToolbar tint on iOS 4 Theorem numbering I am trying to number my theorems, corollaries, Lemmas, Propositions, Definitions, Remarks etc. I put the following code:  \theoremstyle{theorem}  \newtheorem{theorem}{Theorem}[section] \newtheorem{corollary}{Corollary}[theorem] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition}  \theoremstyle{definition} \newtheorem{definition}{Definition}[section] \newtheorem{example}{Example}[definition]  \theoremstyle{remark}     \newtheorem{remark}{Remark}[section]   I want to produce the following:  theorem 1.1  proposition 1.2  definition 1.3  example 1.4  remark 1.5  lemma 1.6  but the code above gives me  theorem 1.1  definition 1.1  remark 1.1  lemma 1.2  Can anyone tell me if there is a code that numbers all these respectively?