If an abelian group has subgroups of relatively prime orders r and s(which are cyclic), there exists a subgroup of order rs?
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
In reading through the original GCM specification (), the composition of the 128 bit Initialization Vector as a concatenation of a 96b nonce and a 32b unsigned wrapping counter seems arbitrary and forces the scrambling pattern to repeat every 232 16-byte block.  Is the algorithm expected to be secure for significantly longer stream lengths if for example the IV were a 128b nonce XORed with a 64b or 128b counter, or are there known cryptanalysis issues that begin to arise? Is it possible to make an EXACT ISO of my system to put on other computers? I am new to linux, but had a question. I am getting in the business of buying old computers, putting Linux on them, then donating them to students who don't have their own computer at home. I have gone through and installed Xubuntu on my system, installed/uninstalled all the software that I want/need, and now want to know if there is a way that I could make an ISO of my system, and put it onto ANOTHER computer, and still have all of my tweaks, and programs ready to go after the ISO has installed. That way I don't need to go through and spend an hour or two on every computer.   What programs would you recommend for creating an ISO like this?   Thanks, Tobin Anonymous Types - Are there any distingushing characteristics? Is there anything to use, to determine if a type is actually a anonymous type? For example an interface, etc?  The goal is to create something like the following...  //defined like... public static T Get&lt;T&gt;(this IAnonymous obj, string prop) {     return (T)obj.GetType().GetProperty(prop).GetValue(obj, null); } //...  //And then used like... var something = new { name = "John", age = 25 }; int age = something.Get&lt;int&gt;("age");   Or is that just the beauty of an anonymous type? Nothing to identify it self because it takes a new shape?  Note - I realize that you can write an extension method for the object class, but that seems like a little overkill, in my opinion. Adverb between conjugated verb and infinitive? The judicial function in considering and applying statutes is one of interpretation and interpretation alone. The duty of the court in every case is loyally to endeavour to ascer­tain the intention of the legislature; and to ascertain that intention by reading and interpreting the language which the legislature itself has selected for the purpose of expres­sing it.    1. What's this phenomenon called? Is this placement unusual or due to  my English's primitiveness?  2. Why not situate the adverb after 'endeavour', or even split the infinitive 'to endeavour' and wedge it in between?  What are the similarities and differences due to a different position? How to calculate the prediction interval for an OLS multiple regression? What is the algebraic notation to calculate the prediction interval for multiple regression?  It sounds silly, but I am having trouble finding a clear algebraic notation of this. More Generating Functions problems Stack Exchange's heavy reliance on external scripts extracting energy from cosmological expansion This question is a more concrete reincarnation of an .  Are there mechanisms to extract energy from the cosmic rate of expansion? putting some extremely long ropes across the universe and extract work from their increase of separation?  assuming this is possible ( i don't see why it would not ), what form would take the back-reaction force? in all physics, every time you extract work from some system by some force, this system will exert a force back. Can we slow down cosmic expansion by variations of these mechanisms? Can I use mirroring to make a copy of my Database? Should there be a comma in 'a 30-day, money-back guarantee'? How to explain the long lifetime of Rydberg atoms with Fermi golden rule? Bugged display in search using negation Difference between standard error and standard deviation I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure the standard error? Why can't I seem to grasp interfaces? Could someone please demystify interfaces for me or point me to some good examples? I keep seeing interfaces popup here and there, but I haven't ever really been exposed to good explanations of interfaces or when to use them.  I am talking about interfaces in a context of interfaces vs. abstract classes. Money from my parents from abroad to my bank account in UK I am from Japan. I have moved to UK recently on a spouse visa.   I still have my Japanese bank account which I have been using even before I came to UK. I have saving in that account and also my parents transfer me some money per month in my bank account in Japan. I have an International Debit Card on this account.  I am withdrawing this Money in UK via ATM / Debit Card.  In this case, do I have to pay taxes in UK or declare this as income in some form. Once a lead is converted it automatically creates an account, contact and one opportunity. But in my case i want to display the result without creating an Account. Please provide me with a sample code.  Any help will be appreciated... The following code gives me an error:  \documentclass[12pt]{article} \usepackage[margin=2cm]{geometry} \usepackage [english]{babel} \usepackage{amsmath, amssymb} \usepackage{enumitem, array} \begin{document} {\begin{minipage}[t]{\textwidth} \begin{enumerate}[label=(\roman*)] {\setlength\itemindent{10pt}\item  \begin{equation*} \begin{array}{&gt;{\centering\arraybackslash}m{1.5cm}&gt;{\centering\arraybackslash}m{1.5cm}&gt;{\centering\arraybackslash}m{1.5cm}&gt;{\centering\arraybackslash}m{1.5cm}&gt;{\centering\arraybackslash}m{1.5cm}}  \hline x &amp; l_{[x]} &amp; d_{[x]} &amp; l_{x+1} &amp; \mathring{e}_{[x]} \\ \hline \end{array} \end{equation*}} \end{enumerate} \end{minipage}} \end{document}   Note: for various reasons, I have to keep minipage there. For some reason, this code gives me an error when it compiles. It gives the following output:     The errors either say there is a } missing or a $ missing. My eyes don't see such a thing! How to test if a player is near coordinates in 1.13? What does the following for loop syntax mean in C? How to vertically align an image inside a div