I have no idea how to approach this.  I'm supposed to use $f\in \mathbb{Q}[X]$ is irreducible $\iff \exists{a}\in\mathbb{Q}$ such that $f(X+a)$ is irreducible.  I tried to use $a = 1 \in \mathbb{Q}$ so  $\frac{(X + 1)^p-1}{X}=(X+1)^{p-1}+\cdots+ (X+1) + 1$  but I don't see how I can get from there to being able to use  any other criterion.
Can someone give me a hint how to the irreducibility of $X^{p-1} + \cdots + X+1$, where $p$ is a prime, in $\mathbb{Z}[X]$ ?    Our professor gave us already one, namely to substitute $X$ with $X+1$, but I couldn't make much of that.
I'm wondering if it makes a difference in interpretation whether only the dependent, both the dependent and independent, or only the independent variables are log transformed.  Consider the case of  log(DV) = Intercept + B1*IV + Error    I can interpret the IV as the percent increase but how does this change when I have   log(DV) = Intercept + B1*log(IV) + Error   or when I have   DV = Intercept + B1*log(IV) + Error   ? I know that IList is the interface and List is the concrete type but I still don't know when to use each one. What I'm doing now is if I don't need the Sort or FindAll methods I use the interface. Am I right? Is there a better way to decide when to use the interface or the concrete type? What would be the easiest way to view classes, methods, properties, etc. inside a jar file? I'm looking for something equivalent to the very useful  Lutz Roeder .NET Reflector  - for Java Can I use an inner tube that's too narrow for the tyre? I recently got a puncture and when I went to replace the inner tube I discovered that I'd bought the wrong size tube. My tyre is 700 x 40c, the tube is 700 x 28-35c.  What is likely to happen if I use this tube? Will the tube explode when I attempt to inflate it? I want to make my appexchange app available in multiple language like Spanish, dutch etc. so that depend on the language of the user they can access the app.  Is it possible in any way..  any help will be appreciated.. Thanks How does Wild Shape work with special ways to calculate your AC? Among the effects of Wild Shapes, these two:     Your game Statistics are replaced by the Statistics of the beast, but   you retain your alignment, personality, and Intelligence, Wisdom, and   Charisma scores. You also retain all of your skill and saving throw   proficiencies, in addition to gaining those of the creature. If the   creature has the same proficiency as you and the bonus in its stat   block is higher than yours, use the creature's bonus instead of yours.   If the creature has any legendary or lair actions, you can't use them.      You retain the benefit of any features from your class, race, or other   source and can use them if the new form is physically capable of doing   so. However, you can't use any of your Special senses, such as   Darkvision, unless your new form also has that sense (PHB p.67, "Wild Shape")   Seem to come into conflict with each other when things like Draconic Resilience:     When you aren't wearing armor, your AC equals 13 + your Dexterity   modifier. (PHB p.102, "Draconic Bloodline")   and Barbarians:     While you are not wearing any armor, your Armor Class equals 10 + your Dexterity modifier + your Constitution modifier. You can use a Shield and still gain this benefit.   and Monks:     Beginning at 1st level, while you are wearing no armor and not wielding a Shield, your AC equals 10 + your Dexterity modifier + your Wisdom modifier.   and Stone Sorcerers:     As an action, you can gain a base AC of 13 + your Constitution   modifier if you aren’t wearing armor, and your skin assumes a stony   appearance. This effect lasts until you end it as a bonus action, you   are incapacitated, or you don armor other than a shield.   How would these resolve? Most Common Aspect Ratio? I'm building a web site that will allow users to upload photos. For design and layout purposes, I need to know the most common aspect ratios users will upload. What is the most common aspect ratio of photos (e.g from dSLR, smart phones, etc.)? Comparing signatures of apks I have two .apk files that are supposed to be different versions of the same app. What is the best way to check if they where both signed with the same key?  I want to make sure no mistakes were done and the newer version would be treated as an update of the same app. Exit strategies for "chameleon questions" I'm not sure if there's already an existing term for this, so I'm inventing my own. (tl;dr: I call them &quot;chameleon questions&quot; because they change every time you submit or edit an answer.  If you're already intimately familiar with the phenomenon, please skip past the first set of bullet points to where I ask for recommendations.)  I think many of us have experienced this on occasion:  You open up a narrow-looking question, usually dealing with some specific error message.  The question probably contains a snippet of sloppy but not quite awful code; code indicating that the author, typically a new/low-rep user, possibly a , doesn't really know what they're doing.  I'm not trying to be condescending here, they're probably very intelligent and hardworking, but in this specific case, they're clearly in way over their head.  However, as a question, it's not really too bad.  The goal and problem are both clearly stated.  The code is formatted (sort of).  Mort was polite and checked their spelling.  The question looks answerable, although from a rep perspective* it's an obvious dead-end, it's had maybe 3 views in the past 30 minutes.  So you decide, you know what, this person took the time to write up the question properly, they deserve an answer, put on your good citizen hat and throw them a bone.  You slog through the ugly code, find the offending line, direct their attention to it and explain why it's wrong and how it needs to be fixed.  Later, they leave a comment saying that yes, that was indeed the problem and your answer helped them fix it (great!).  Oh, but, now there's another problem (uh-oh...). Something else is broken.  After letting out a long sigh, you read the comment and/or edited question, roll up your sleeves, and write up Take 2, hoping that's the end of it.  And of course it's not the end.  Now maybe the error is gone, but it's not doing what it's supposed to.  If you're anything like me, your patience is now starting to wear thin. It's lousy code and you didn't volunteer to help them rewrite their whole app.  And of course, the question still only has 12 views, and nobody has upvoted either the question or your answer, including the person you're helping, so this is turning out to be a genuinely thankless task in all respects.  Welcome to &quot;Family Tech Support&quot;, Web 2.0 Edition.   * Which is of course just an arbitrary number that none of us care about. Not really, anyway. Not very much, at least.  So, here's where I get to my question.  At this point, do you:  Leave a comment, stating as politely as possible that you've done your best to help them answer the original question they asked, and if they have a new problem then they should start a new question?  (I did this once, and actually ended up with an accept, but I felt kind of guilty afterwards, I don't think anybody answered their 2nd question).  Bite the bullet and edit your answer a 3rd, 4th, 5th time, however many times it takes to resolve their issue, knowing full well that they may not even remember to accept the answer once you're done? (I may work for free on SO, but that doesn't mean my time is worthless.)  Just abandon the question, hoping that it will force Mort to start thinking for himself?  Something else?   I've tried all three of the above and none of them ever quite feel right. I do want to help, but at the same time there are a lot more &quot;lucrative&quot; questions I could be answering. And I don't mind spending a lot of time on an answer either, if the question is interesting or important to me, but debugging is dull work. I'd prefer not to reference specific questions here; I'm pretty sure that this is a shared experience, and my objective isn't to point fingers at &quot;misbehaving&quot; members.  I'm more looking for some practical advice on how to dig myself out of these pits of despair. Anybody have any other ideas? Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$? Making overview with linked detailed maps in QGIS? Showing this metric space is complete Let $X=(0,1]$ and $d(x,y)=\left|\frac{1}{x}-\frac{1}{y}\right|$. I've proven $(X,d)$ is a metric space but I don't know how to show its completeness. How can I do that? How to determine callee function name in a script To make it short, doing something like:  -bash$ function tt {  echo $0; }  -bash$ tt   $0 will return -bash, but how to get the function name called, i.e. tt in this example instead? "Speed" of Gravity and Speed of Light I know that for every $n\in\mathbb{N}$, $n\ge 1$, there exists $p(x)\in\mathbb{F}_p[x]$ s.t. $\deg p(x)=n$ and $p(x)$ is irreducible over $\mathbb{F}_p$.     I am interested in counting how many such $p(x)$ there exist (that is, given $n\in\mathbb{N}$, $n\ge 1$, how many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$).   I don't have a counting strategy and I don't expect a closed formula, but maybe we can find something like "there exist $X$ irreducible polynomials of degree $n$ where $X$ is the number of...".  What are your thoughts ? Light clock with mirrors on a moving train Flag and close my own question Why is it possible to flag and close my own question?   The only realistic usage I could think of is when I see that my question is a duplicate, but it has already got some great answers. So instead of deleting the question, I would vote to close it as a duplicate.   But still, I can't see how flagging my own question would be useful. Is “all women who are mothers of daughters” right? Is the expression      All women who are mothers of daughters are here.   correct? I mean every woman who has at least one daughter is here. Table of Contents for poetry collection (ConTeXt) I'm getting stumped about how to generate the ToC for this book. I'm about to give up and just do it by hand. The author wants to include a lot of structural information that isn't present in the actual text, and none of the numbers "roll over" as they're want to do in ConTeXt.  This is the desired effect:    Narrator 1...      FIRST PART: PART SUBTITLE  1). First Poem // First Poem (Spanish title) . . . . . . . . . . . . . . . . .    1     Author of Poem (b. XXXX d. XXYY)  2). Second Poem // Poema Secunda . . . . . . . . . . . . . . . . . . . . . . .    3     Author of Poem    Narrator 2...  3). Third Poem // Third Poem . . . . . . . . . . . . . . . . . . . . . . . . .    5     Author      SECOND PART: Part 2  4). Fourth Poem // Fourth Poem . . . . . . . . . . . . . . . . . . . . . . . .    7     Author    Narrator 3...   The problems I have essentially boil down to these:   There is this weird "narrator" concept that doesn't seem to contain or be contained by the part/poem structure. A new part doesn't imply a new "narrator" and a new "narrator" doesn't imply a new part. I need to aggrandize each title with the title in translation and the author, and I want to typeset them nicely. I need poems to continue counting up across parts.   I see basically three approaches:   Make each poem a chapter and customize the appearance with \setuphead[chapter][....]. Then use \writebetweenlist[chapter] to add the Narrator and author information. Make a new list with \definelist[poem] and \definecombinedlist[content][part,poem]; continue using \writebetweenlist[poem] to insert the author and Narrator. This feels like the most conceptually valid option, but I think I'll still need a lot of customization. Forget all about ConTeXt and switch to plain TeX, use eplain's writetocentry system. Make it look right and forget maintainability. Syntactic characterisation of the intersection of CTL and LTL