Find the remainder when $11^{12}$ is divided by $13$.
How to use Fermat's little theorem to find $50^{50}\pmod{13}$?
How to set mount point of boot partition to /boot/efi? What is a StackOverflowError? I'm wondering how to approach duct work, piping, and wiring? In the past, I have used the spin tool to make corners, but I find it very cumbersome. How do you do duct work and piping? I have seen people use curves, but I find it's hard to get straight 90 degree angles or just uniform angling across the whole model. It's also hard connecting piping together if they started from different locations. Here's some reference: How does the current limiting resistor for an LED affect current and voltage drops? I'm having a bit of trouble understanding currrent limiting resistors in simple LED circuits. I know that I can determine the optimal resistor like so:  \$\displaystyle R=\frac{V_{s}-V_{f}}{I_{f}}\$  But I'm having a hard time understanding how this one value modifies the voltage and the current to the correct values for the LED. For example, if my calcuations for a super bright blue LED (with \$V_{f}\$ being 3.0-3.4&nbsp;V and \$I_{f}\$ being 80&nbsp;mA, and a voltage source of 5&nbsp;V) gives me 25&nbsp;ohms (using the lower bound of the forward voltage), that's fine. So the current throughout should be 80&nbsp;mA and the voltage drop for the resistor and LED should be 2 and 3 volts, respectively.  But what if I used a 100&nbsp;ohm resistor instead? Or any other value—how would I calculate the voltage drops and current? Would I assume one of them stays the same? automatically apply special formatting to selected words in text Possessive of a word that is already possessive How to access a usb flash drive from the terminal? I only have access to the command line. I need to backup my data (on the user folder) to a pen (USB DOK).    How can I mount a flash drive manually? What should be the copy command? Command for taking a screenshot to a new file When should titles like "captain" or "admiral" be capitalized? Please excuse the contrived example below, but I am wondering if this example is properly capitalised? I'm assuming that capitals are used when addressing someone directly, but lower case is used elsewhere. Can someone give some rules on this?      The captain walked into the room.    "Hi, Captain," said the admiral.   "Hi, Sir," replied the captain.   "Call me Admiral."   "Hi Admiral."   The captain and admiral stepped forward.   "Prime Minister, this is Captain Jones," said Admiral Brown.   "Pleased to meet you," said the prime minister. How do I make a 3 dimensional character out of flat picture? I have a cartoon character (a lion) that is part of my business logo that I want to put into Blender and animate it somehow. Is there any way I can take a flat picture (JPEG) and transform it into a 3D image and then animate it in Blender? I'm reading that a 50mm lens is recommended as a first prime lens for DSLR owners as it's supposed to give a 'natural' perspective, but when used on (most) DSLRs, the view is cropped, as if you were zoomed in by 1.5-1.6x, so it's more of a telephoto lens when used on a DSLR. I've also read however that the 50mm lens gives the same perspective on a DSLR and a 35mm, and shouldn't really be considered to be 'equivalent' to an 80mm lens as the crop factor isn't really a magic focal length changer.  Can someone explain how the image is different from (for example) a 50mm lens on a DSLR and an 80mm lens (assuming 1.6x crop factor) on a 35mm camera? Calculate the last digit of $3^{347}$ I think i know how to solve it but is that the best way? Is there a better way (using number theory). What i do is: knowing that  1st power last digit: 3 2nd power last digit: 9 3rd power last digit: 7 4rh power last digit: 1 5th power last digit: 3    $3^{347} = 3^{5\cdot69+2} = (3^5)^{69} \cdot3^2 = 3\cdot3^2=3^3=27 $ so the result is $7$. How do you reverse a string in place in C or C++? How do you reverse a string in C or C++ without requiring a separate buffer to hold the reversed string? Most of something is plural or singular? I am writing a literature review. My question is which sentence is correct?   Most of the existing work focus on... Most of the existing work focuses on ... Most of the existing studies focus on ...   Thanks The limit of reciprocal is the reciprocal of the limit While I was reading the book Exploratory examples for real analysis, I came across this:     to show that : $$\lim_{x\rightarrow x_o}\frac{1}{h(x)} = \frac{1}{\lim_{x\rightarrow x_o}{h(x)}} = \frac{1}{M}$$      Discussion:Let $\epsilon \gt 0$.we want to find $\delta \gt 0$ such that       if  $0 \lt |x-x_0| \lt \delta $,then $\Big|\frac{1}{h(x)}-\frac{1}{M}\Big|\lt \epsilon$.      In order to get expression involving $|h(x)-M|$,we first find the common denominator:        $\Big|\frac{1}{h(x)}-\frac{1}{M}\Big|=\Big|\frac{M-h(x)}{M~h(x)}\Big|$      $~=\Big|\frac{h(x)-M}{|M|~|h(x)|}\Big|$.      As we have to deal with variable term $|h(x)|$ in denominator.We can construct bound .Let $\epsilon =\frac{|M|}{2}$ ,since lim$_{x\to x_o}h(x)=M$,there exists $\delta_1\gt 0~~$ s.t.       if $0 \lt |x-x_0| \lt \delta_1 $,then $|h(x)-{M}|\lt \frac{|M|}{2}$.      As you study steps below,identify that step where $h(x)\neq 0$ for all $0 \lt |x-x_0| \lt \delta_1 $ plays a critical role:      $|M|=|M-h(x)+h(x)|$      $~~~~~~\leq |M-h(x)|+|h(x)|$      $~~~~~~= |h(x)-M|+|h(x)|$      $~~~~~~\lt \frac{M}{2}+|h(x)| \implies$      $\frac{|M|}{2} \lt |h(x)| \implies$      $\frac{1}{h(x)}\lt \frac{2}{|M|}$,where $0 \lt |x-x_0| \lt \delta_1 $.      Now that we've bound for $1/h(x)$,we can apply the definition to term $|h(x)-M|$.      Since     lim$_{x\rightarrow x_o}h(x)=M$,we can find $\delta_2 \gt 0$ such that,       $~~~~~~~~~~~~~~~~~~~~~~~~~~~~$if  $0 \lt |x-x_0| \lt \delta_2$, then $|h(x)-M|\lt \frac{|M|^2 \epsilon }{2}$   The thing I can't understand is for what purpose did the author work with such complicated expression involving $\epsilon $ in the end of the discussion? Why Smart's attack doesn't work on this ECDLP? How to install Ubuntu on a Mac and keep OSX? Could anyone provide a concise step by step instruction on how to install Ubuntu 12.04 on a Mac OS X Lion?  I have read that Ubuntu corrupts the EFI file so I would like to hear from those who have successfully done it. Integral $\int\csc^3{x} \ dx$ How to calculate the prediction interval for an OLS multiple regression? What is the algebraic notation to calculate the prediction interval for multiple regression?  It sounds silly, but I am having trouble finding a clear algebraic notation of this. Why does James Bond use his real name? In the James Bond universe most characters go by a code name M, Q, the various 00s, In Skyfall Silva is a made up name.  Others such as Tanner, Robinson and Moneypenny, Trevelyan we're not so sure but we've got no reason to believe they're real.  However Bond uses his own name - we've even seen the grave of his parents to confirm this.  Why does Bond use his real name and (as far as we know) no one else does?