For every integer n, if n is greater than or equal to m, then n^5 - 1 is composite. Statement: For every integer n, if n is greater than or equal to m, then n^5 - 1 is composite. What is the smallest possible integer m &gt; 1 to satisfy this statement?
Prove that $x-1$ divides $x^n-1$ In algebra &amp; polynomials, how do we prove that $$x-1 \mid x^n -1?$$
How to change the size of desktop icons? I tried gconf-editor as given at  .  I am not getting the option for changing size at app &gt; nautilus &gt; icon_view.  I am using Ubuntu 11.10. Kindly help me in changing default icon size.   I want to make them small. How can I tell whether beetroot is still edible? I have some raw beetroot I bought about a week ago, having stored them at room temperature since. It's the first time I bought it raw, and I'm unsure whether it's still edible.   It is already soft, and when I cut it, it smells... Well, different than I expected. It's not a rotten smell as such, but it's nothing like the sweet beet-rooty smell I know from the pre-packaged, pre-boiled supermarket variety.  How can I tell whether it's still safe to eat? I have a matrix:  $$ A=\begin{bmatrix}1 &amp; a \\ 0 &amp; 1\end{bmatrix} $$  which satisfies: $A\left( e_{1}\right)=e_{1},A\left( e_{2}\right)=ae_{1}+e_{2}, a\neq 0$  I need compute all powers $A^{n}, n\in \mathbb{Z}$ and find their matrices.  $$ A^n= \begin{bmatrix}1 &amp; na \\ 0 &amp; 1\end{bmatrix} $$  Is it true?  Is there a basis of $V$ (if $V$ is a 2-dimensional real vector space with basis $\left\{e_{1},e_{2}\right\}$) so that the matrix of $A$ is diagonal? How many integer solutions does $xy+9(x+y)=2006$ have? Here $x$ and $y$ are both integers.  My trying:        I have tried to solve this problem. But I have no idea to solve this. Please help A guide to moderating comments Question about preposition -of- New flagging dialog has a duplicate for duplicate We've changed the flagging format from today(AFAIK) as below,        looks good.  But, when I select it should be closed for another reason...  I can see the same reason duplicate on the top.        What is the need of placing that reason over there? It should not be there. Please remove the dupe. How do I execute for a player wearing armor with a colored name I am working on a command block contraption on my server that involves armor giving you certain potion effects.  /execute if entity @p[nbt={Inventory[{Slot:100b,id:"minecraft:leather_boots",tag:{display:{Name:"{\"text\":\"Frog Boots\"}"}}}]}] run effect give @s jump_boost 1 1 true  However, it only works if the boots are named in an anvil. How would I write the command if I wanted to test if the player was wearing boots named "Frog Boots" in bold and green text? What's the tax on a hobby orchard? $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$ Let $p(z)= \sum_{k=0}^n a_k z^k$ ,  $a_n \neq 0$ , be a polynomial of degree $n$ such that $|p(z)| \leq M$ for $|z| \leq 1$.  Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$  This was an exam question. Part (a) of this question asked the converse: if $|p(z)| \leq M|z|^n$ and $|z|$ is sufficiently large, then $p(z)$ is a polynomial. This question came straight out of Ahlfors' Complex Analysis, which I solved by showing, using the Cauchy Estimate,  $|p^n (z)|  \leq \frac{n!M|z|^k}{R^n} = 0$ as $R \to \infty$.   I would like to work backwards with this.   May I do this, or similar:   $p(z) = \frac{1}{2\pi i} \int_{c} \frac{f(\zeta)d\zeta}{\zeta-z}$  $\Rightarrow  |p(z)| \leq \frac{2\pi M|z|^n}{1(2\pi)}= M|z|^n$ Remove completed reminders in OS X and iOS I have two tables, both with start time and end time fields. I need to find, for each row in the first table, all of the rows in the second table where the time intervals intersect.  For example:             &lt;-----row 1 interval-------&gt; &lt;---find this--&gt; &lt;--and this--&gt; &lt;--and this--&gt;   Please phrase your answer in the form of a SQL WHERE-clause, AND consider the case where the end time in the second table may be NULL.  Target platform is SQL Server 2005, but solutions from other platforms may be of interest also. Word for the behavior of people who complain at everything you do I currently have a valid Schengen tourist visa that expires next year, issued by the French Consulate in Saudi Arabia.   I am going to a 60-day study abroad program in Italy and they require a student visa. I went to the Italian Consulate in Boston and they asked me to go to the French Consulate and cancel my visa. However, the French Consulate said that I needed to contact the French Embassy in Saudi to cancel the visa.   How can I cancel my tourist visa if I am currently in the United States? My Italian student visa application is due tomorrow morning. I am trying to install Linux headers for Kali Linux on my machine and I have tried every possible solution on the internet but it always show "Unable to locate packages "  root@kali:/usr/sbin# apt-get install linux-headers-4.6.0-kali1-amd64 Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package linux-headers-4.6.0-kali1-amd64 E: Couldn't find any package by glob 'linux-headers-4.6.0-kali1-amd64' E: Couldn't find any package by regex 'linux-headers-4.6.0-kali1-amd64'   Here is my sources.list file :  # Regular Repositories deb http://http.kali.org/kali sana main non-free contrib deb http://security.kali.org/kali-security sana/updates main contrib non-free # Source repositories deb-src http://http.kali.org/kali sana main non-free contrib deb-src http://security.kali.org/kali-security sana/updates main contrib non-free   Uname -a output :   root@kali:/usr/sbin# uname -a Linux kali 4.6.0-kali1-amd64 #1 SMP Debian 4.6.4-1kali1 (2016-07-21) x86_64 GNU/Linux How to convert milliseconds into human readable form? Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$. Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.   This is a homework question, and I understand that its part of Fermat's Last Theorem, but when I looked that up to try to figure out the homework, I realized that it is way further than what we've learned in class so far. We have to prove this, but the only way I can think to do it is by exhaustion, which would be extremely lengthy. Any little shove in the right direction would be appreciated. Thanks! No reason for anyone to see pending close votes, except OP (and maybe people who already voted) Are ores replenished over time? Notation for infinite product in reverse order