Show that $x^{p^n}-x$ is the product of all monic irreducible polynomials in $\mathbb{Z}/p\mathbb{Z}[x]$ of a degree $d$ dividing $n$.
Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?
I have just updated (through Software Update) to Ubuntu 16.04 LTS from 15.10. There are random instances of screen flickering throughout usage. After noticing this issue, I installed Compiz Config Settings Manager, selecting Force fulls screen redraws (buffer swap) on repaint, which did nothing.   Is there any way this could be related to compiz settings or is this another issue?    EDIT: not fixed after clean install, upgrade to kernel 4.5.2, however screen flickering is reduced, it is every now and then (10 minutes apart). I will see if upgrading to kernel 4.6.0-994-generic will fix this.     EDIT: fixed as of kernel 4.6.2 generic,  currently running 4.7.2 without any issues. Setting or modifying a (system wide) environment variable in cmd.exe I am looking for a convenient way to add and/or modify and/or delete an environment variable from the command line. Particularly, I find myself at times in situations when I have to add a few variables in cmd.exe.  I'd be grateful if someone showed me a non-GUI way to modify (that is: to add a new directory to) the %PATH% variable.  The change should be be permanent, not just for duration of the cmd session. Why didn't Snape keep or secure his copy of Advanced Potion-Making? How to remove illegal characters from path and filenames? Android: textview hyperlink JSF 2.0 File upload Why isn't this sudo mv operation with wildcard working? What is the music on S3E16 when Todoroki was fighting group of ninjas? When I post an answer to a brand new question I usually find that someone else has submitted that same answer just moments before. (, usually ;-) )  What I've started to do lately is (I think) the right thing.   If I notice that another answer predates mine, and that I add no value over it, I immediately delete my own answer, and upvote the other guy.  I recommend that you too do the same. Otherwise the message will be diluted.  Similarly, if after posting your "answer" you realise that you are in fact wrong (and you've just misread the question) -- you can actually delete your answer.  Is this reasonable?  (The reason why I'm writing this down is because it feels completely counter-intuitive to delete your own stuff. But it really saves everyone time and effort) How do I survive in the Underworld? Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$ Let $a, b, c \in \mathbb{N}_0$. If $a+b+c=12$, how many solutions $(a,b,c)$ satisfy the equation?   Is the answer:      $729$ Why is a black hole black? Polynomial rings in infinitely indeterminants How can we prove that (the set of all polynomials in infinitely non commutative indeterminants over $k$) is a ring, where $k$ is a ring with unity?   Adding two polynomials is a polynomial, but for commutativity  How can we show the following: $ax_1+bx_2=bx_2+ax_1$ (commutativity of addition) If we have finite number of variable it is easy to prove it, (we take the $n-1$ variables...), but what about the infinite number of variables?  Can someone give me a hint? how to host multiple pages from diferent domains all together? What 70s (60s?) TV show / TV movie had a generation ship whose inhabitants did not know they were on a spaceship? I have the vaguest memory of a TV show (maybe a BBC import?) in which the protagonists were moving through the sections of a massive generation ship whose inhabitants had forgotten that they were on a spaceship... I know there was an RPG with the same plot (which, after all, is a pretty great blank slate) but I definitely feel I saw this on a static-filled 13" B&amp;W TV back in the day... Forcing series convergence If a warlock's invocation states that they can use a spell without a slot does that mean they can cast the spell as often as they want? On page 111 of the 5E hand book the invocations Misty Visions, Mask of Many Faces, Master of Myriad Forms, and Otherworldly Leap all they that you can cast them without expending a spell slot. Does this mean the spells essentially become cantrips and I can cast them as often as I want? Unicoin Bug: Automining Returns Diminishing I'm using the auto-mining script from one of the meta posts here and it doesn't works!  At first I got steady returns but the returns seem to diminish over time. Using Fiddler I confirmed that the server seems to release less and less coins.  This is unacceptable! I am a loyal customer paying nothing and I demand that my auto-mining script continues to yield returns forever!  If you cannot deliver on that please refund what I have payed for using this site.  Plz advise!    In case you didn't notice: This is a parody of over-demanding, leeching askers on Stack Overflow. I recently renewed my passport. I also have an expired passport which has my Canada visa (visitor's) valid for another three years. I have already used my Canadian visa which is multiple entry. I am planning to visit Canada this summer.  Since my valid Canadian visa is in my old/expired passport, do I need to renew/transfer my Canada visa or can I simply travel with valid visa in old passport? Double and triple substitution in bash and zsh Follow-up to the background part in .  In bash I can use ${!FOO} for double substitution, in zsh ${(P)FOO}. In both, the old-school (hack-y) eval \$$FOO works.  So, the smartest and most logical thing for me would be ${${FOO}}, ${${${FOO}}}… for double/triple/n substitution. Why doesn’t this work as expected?  Second: What does the \ do in the eval statement? I reckon it’s an escape, making something like eval \$$$FOO impossible. How to do a triple/n substitution with that that works in every shell?