How to prove that $x^2+1=5^y$ has no positive integer solutions for $y\geq 2$?
On equations $m^2+1=5^n$
How to do volumetric lighting for a forest scene? Are all limits solvable without L'Hôpital Rule or Series Expansion Is it always possible to find the limit of a function without using  or ?  For example,   $$\lim_{x\to0}\frac{\tan x-x}{x^3}$$  $$\lim_{x\to0}\frac{\sin x-x}{x^3}$$  $$\lim_{x\to0}\frac{\ln(1+x)-x}{x^2}$$  $$\lim_{x\to0}\frac{e^x-x-1}{x^2}$$  $$\lim_{x\to0}\frac{\sin^{-1}x-x}{x^3}$$  $$\lim_{x\to0}\frac{\tan^{-1}x-x}{x^3}$$ Displaying equations, how to combine strings and values without evaluating everything. Why are 15 reputation points required to upvote? I think more reputation points should be required to add a new answer than to upvote an existing answer.  I don't continually watch for new questions, so usually when I find a question it has already been answered.  It seems bit inappropriate to answer an already-answered question in order to contribute to the conversation, but until you earn reputation, you can't upvote or comment; you can only add new answers, which prevents me from contributing at the moment as much as I would like to.  This seems backwards to me. If someone incorrectly upvotes a bad answer, the damage is minimal, as other users can down vote it and upvote the correct answers. On the other hand, an incorrect answer wastes the time of everyone who reads it.  So, IMHO, it should require more reputation points to add an answer than to upvote or comment on an existing answer.  I wouldn't say say that users should be prevented from answering unanswered questions until they have x reputation points, as that might prevent users who have answers from providing them, but perhaps it should be required if the question is already answered, to discourage users from reiterating previously given answers.  What do you think? I'm talking about this nonsense:   Now, I'm aware that there are problems with the practicalities (or possibilities) of methods involving exotic matter with negative mass, and that kind of thing has been addressed here:   But in this case my question is different and more specific. Sweeping all the other problems of constructing such a beast under the rug, wouldn't this violate causality?  SR says that the simultaneity and relative ordering of events is dependent on the relative motion of the observer, but that no matter how it works out, if event A causes event B, no observer will see B first. One of the many problems with FTL travel (or signals) is that if any information is sent faster than light, there will exist an inertial frame in which the signal arrives before it is sent, a blatant violation of causality. (I think we can all agree, can we not, that the threshold should be extremely high before breaking assumptions that we're in a causal universe?)  So how is any scheme to travel faster than light, even if it may locally satisfy the equations of GR, not a blatant violation causality according to SR?  Is my understanding of GR incomplete and there's something in it that obviates the causality implications of SR? Or am I correct that FTL claims should be dismissed with extreme prejudice on this basis alone? (Pending a serious replicable experiment showing causality to be breakable.) Why is pruning not needed for random forest trees? Breiman says that the trees are grown with out pruning. Why? I mean to say that there must be a solid reason why the trees in random forest are not pruned. On the other hand it is considered very important to prune a single decision tree to avoid over fitting. Is there some literature available to read for this reason? Of course the trees may not be correlated but there still will be a possibility of over fitting. Of course when you type:  sudo apt-get install whatever   It asks you:   Do you want to continue [Y/n]?    Is there any way I can just install it without it asking me if I want to continue? I don't really care about space, I have more then enough. Show Log of the Sql statements that QGIS generates to retrieve Data from Postgis Is there a ways to  - make QGis log its generated SQL Statement or to - force POSTGIS to log all interaction with QGIS?  There is something strange happening to the WFS layer I retrieve in QGIS, since it does  not select all data available in the respective database table. I need to find out, what criteria QGIS chooses in order to narrow down the select set. Preprocess categorical variables with many values I have a dataset that consists of only categorical variables and a target variable. I want to predict the (binary) target variable with the categorical variables.  I am trying to do this in Python and sklearn.  The categorical variables have many different values. I was thinking to create dummy variables for each value in all the categorical variables. However, in the end this results in a sparse data set with thousands of variables.  How would you go about to reduce the number of dummy variables? Would you use Chi2 to select useful features?  Or would you not make dummy variables at all? Permanently remove/disable Touch Keyboard in Windows 8 taskbar? Is there a name for this layout? Every time since a few days ago after I caught Mespirit, when I go to the portal in the Nameless Cavern and I press A to interact. All that happens is a short dialog sequence and nothing else. I know the requirements are along the lines of having 3 max happiness Pokemon with you in your party which I do. I have also downloaded the recent update/patch from the eShop if that helps at all. How can I make Uxie and Azelf appear in the cavern? Stop terminal auto executing when pasting a command Right, this is a slightly annoying feature because something this happens, and other times it doesn't, very odd.  I paste a command into the terminal with a view to tweaking its arguments, and sometimes it executes the second I paste it. Sometimes it doesn't.  This ranges from embarrassing ( posting nonsensical comments on an IRC ) to dangerous.   How can I shut this feature off for good? I never, never, never want the terminal to auto execute when I paste to it. Which computer science / programming Stack Exchange sites do I post on? App crashes, dock icon remains, can't reboot, yet no process in ps aux to kill In Harry Potter and the Sorcerer's Stone, Nearly-Headless Nick and some other ghosts can visit the Hogwarts students, but why can't other deceased people - such as Harry's parents? How to do power series expansion What is the coefficient of $x^{11}$ in the power series expansion of $\frac 1{1-x-x^4}$?    How do I do power series expansions? Rules for "on", "at", and "in": preposition of time Gauss's Law with Moving Charges Use second argument for optional first argument if not provided in macro I'm trying to construct a command with one optional and one mandatory argument and I'd like the default if the optional argument is not provided to be #2.   Why does this not work?  (error: Illegal parameter number ...)  \documentclass{article}  \newcommand{\mycommand}[2][#2]{\label{#1}#2} \begin{document} \mycommand{mytext} \end{document}   And what would be a way around it?   EDIT: For clarification of my specific use case: I'm trying to define a command that passes a variable on as an option to an environment along those lines, where myenv can have options like optionone=X or optiontwo=Y so the default for the optional #1 should be optionone=#2 (not literally #2).   \newcommand{\mycommand}[2][optionone=#2]{\begin{myenv}[#1]\input{#2}\end{myenv}}   Maybe there's generally a better approach?   (The environment definition I'm using is from .)