I'm still kinda new to number theory so could someone tell me if my solution is right?   Reducing $\mod n +10$  $$n \equiv -10 \pmod{n+10} \implies n^3 + 100 \equiv -900 \pmod{n+10}$$ So we want $(n+10) \mid 900$ and the largest number would be $n = 890$
What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$  I tried to factorize $n^3+100$, but $100$ is not a perfect cube. I wish it were $1000$.
When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes? If $\sum (a_n)^2$ converges and $\sum (b_n)^2$ converges, does $\sum (a_n)(b_n)$ converge? If $\sum (a_n)^2$ converges and $\sum (b_n)^2$ converges, does $\sum (a_n)(b_n)$ converge?  Could someone help me to solve this or at least give me a hint?, I have tried using Cauchy's criterion, the Dirichlet test for convergence, etc, but I can´t prove it.Honestly I don´t know where to start. Any help will be appreciated. Compiling C code in the terminal I've been having a problem with compiling.   I used the following test C code below and saved it as test.c in Home folder.  #include &lt;stdio.h&gt; int main() {   printf("Bruh!");   return 0; }   When I run in terminal the code   gcc test.c -o test   I get  nothing.  Thank you disconnected phone while installing ROM I recently tried to install a custom ROM in my samsung j6+ but halfway through it my PC turned off. Then the problem starts i decided to reboot my phone but it shows this error &quot;No command&quot; &quot; #Reboot recovery cause is [[check_bootmode]RebootRecoveryWithKey]# Block-based OTA Supported API: 3 # MANUAL MODE v1.0.0# E:Failed to mount / cache: Invalid argument  The error message keeps appearing for just a fraction of a second then disappear and appear again I tried to go to recovery mode but no luck i cant get to it I drained the battery to turn off the device then go download mode but after get to it, it also keep restarting help me please. thank you The definite article implying the generic idea of something I have a question about the pattern "turn &lt;something&gt; on &lt;somebody&gt;" :     Then he allegedly turned the body-building equipment on his 44 year-old wife, identified by sources as Feng Liang, and his elderly mother-in-law, Feng Kun Zaehng,77, the sources said.     I understand the phrase "*turn the gun on &lt;somebody&gt;", am not sure about "turn the equipment on &lt;somebody&gt;".  Could the example be wrong? Why is $H(k\mathbin\Vert x)$ not a secure MAC construction? Derivation of binomial coefficient in binomial theorem. How was the binomial coefficient of the binomial theorem derived?  $$\frac{n!}{k!(n-k)!}$$ How to upgrade from 18.10 to 19.10, using the command line? I'm trying to upgrade from 18.10 to 19.10, using sudo do-release-upgrade however I only get an error: An upgrade from 'cosmic' to 'eoan' is not supported with this tool. I performed the steps to update my sources.list to point to old-release server, as suggested here:  This did not help. I get the same error. I am trying to prove that the affine hull of a set $X \subseteq \mathbb{R}^d$ is equal to the affine hull of the clojure of that set: $$ \text{aff}(X) = \text{aff}(\text{cl}(X)). $$  Proving $\text{aff}(X) \subseteq \text{aff}(\text{cl}(X))$ is easy, but containment in the other direction is harder.  I am assuming there is a sequence $\{ x_k \}_{k=1}^\infty \subseteq X$ such that $\lim_{k\to \infty} x_k = x^*$. The point $x^*$ is obviously contained in $\text{aff}(\text{cl}(X))$. But I am not sure how to show it is also in $\text{aff}(X)$, specifically because I am not sure how to show that $x^*$ lies on a line connecting two points in $X$.  Any suggestions on how to surmount this hurdle are welcome. Gmail filters/labels: Force email to stay in Inbox? GIS Point or discrete longitude and latitude columns? How do you calculate this limit $\lim_{n\to\infty}\sum_{k=1}^{n} \frac{k}{n^2+k^2}$? How to find the value of $\lim_{n\to\infty}S(n)$, where $S(n)$ is given by $$S(n)=\displaystyle\sum_{k=1}^{n} \dfrac{k}{n^2+k^2}$$   is unable to calculate it.  This is a question from a questions booklet, and the options for the answer are--  $\begin{align} &amp;A) \dfrac{\pi}{2} \\ &amp;B) \log 2 \\ &amp;C) \dfrac{\pi}{4} \\ &amp;D) \dfrac{1}{2} \log 2 \end{align}$ 'locate' command in terminal. Why is it so fast? I have the following diagram:    However, this looks a bit ugly, I would like a version that looks a little bit better. For example, size the last arrow such that the T_\phi is moved to the right.  This is the code which I am using to do this:  \begin{align*}   \xi \colon &amp;\lb \to \mathcal{L}(\hh)\\   &amp;\phi \mapsto T_\phi. \end{align*}   Where \lb and \hh just give the names for those spaces. Does anybody have a suggestion how I would improve the look of this function definition? Visiting Iran as a dual EU-American citizen A single word or phrase for something that necessarily causes both harm and benefit? What is a single word, or phrase, for something that necessarily causes both harm and benefit? For example, a coal-fired power plant will harm human health through air pollution, but will bring electricity and economic development to a poor area. How do I determine the size of an object in Python? What happens if Superman is near a white dwarf star? With the Superman lore, we know that light from a yellow star gives him his powers, light from blue stars makes him stronger, and light from red stars weakens him.  However, what happens if he is near a white dwarf, or a neutron star?  Has there been any evidence of Superman visiting a star system that wasn't red/yellow/blue? Is there a way to get correctly aligned print export with OpenLayers plugin? I am a beginner using QGIS (1.8.0 Lisboa) on a Mac (OS X 10.6.8 Snow Leopard). I work on a file with two layers in the following sequence (top to bottom):    a vector polygon layer with a few outlines of various buildings in France and Italy (CRS: EPSG:4326 - WGS 84 - "on the fly" re projection is activated ) a Google satellite layer uploaded via open layer plugin.   Sometimes when changing the scale (scrolling in and out) the Google layer updates a little wrong in size or position compared to the polygon layer. But as soon as I "pan" the map everything reconstructs right. Now the problem I have concerns the print composer.  The result of any kind of export - pdf, or image or svg - of my map (vector layer + Google layer in the background) differs from what is shown in the preview of the print composer: the vector layer and the Google layer positions are mismatching and in a different scale. I can send some pictures showing screenshots of the print composer preview and the final results if required.  I tried almost everything:    new files with different CRS settings "cache" update preview "render" update preview different paper sizes,  different scales,   The problem appears only using an open layer map (Google, OpenStreetMap...). If I try the same using two vector layer (shapefile) - one with the buildings, another one with the city in background - everything works out great.  ...exasperating! Since it is a real important research project I would be very grateful for some help and tips.