Let $x$ and $y$ be integers such that $2x+3y$ is a multiple of $17$. Show that $9x+5y$ must also be a multiple of $17$.  So $2x+3y \equiv 0 \pmod{17}$. Adding $7x$ and $2y$ we have that $9x+5y \equiv 7x+2y \pmod{17}$, thus we would need to show that $7x+2y \equiv0 \pmod{17}$. How should I approach this? I cannot see to be able to show the last congruence...
I'm having some trouble understanding a proof on  on Number Theory and I was wondering if you guys could give me some help. The problem is that I don't understand the last implication on the proof for example 1.1     Example 1.1. Let x and y be integers. Prove that 2x + 3y is divisible by 17 iff 9x + 5y is divisible by 17.      Solution. 17 | (2x + 3y) ⇒ 17 | [13(2x + 3y)], or 17 | (26x + 39y) ⇒ 17 | (9x + 5y)       conversely, 17 | (9x + 5y) ⇒ 17 | [4(9x + 5y)], or 17 | (36x + 20y) ⇒ 17 | (2x + 3y).   My problem is that I don't understand how does 17 | (26x + 39y) imply 17 | (9x + 5y). If you could elaborate on this step I would be most grateful.  I'm sorry if this is an obvious question but I am a beginner and I just can't get it.  Thanks for your help in advance.
First, my understanding is that the long-term capital gains tax rate is 0% for those whose marginal rate on ordinary income is 10% or 15%, and (ignoring the highest 39.6% bracket) the rate is 15% for everyone else. (See  and .)  My interest is in what happens at the crucial break between the 15% and 25% bracket, which is $73,800 for married/joint returns in 2013 (and presumably will be higher in 2014, though I haven't been able to find out what that is or if it has even been set yet). Let's say a household has $64,000 in wage income, and sells stock for a $10,000 profit.   Does their income for the purposes of establishing their tax bracket go to $74,000? If so, is the entire $10,000 profit subject to the 15% long-term capital gains rate? Is any part of the wage income subject to the higher marginal tax rate?   Since the amount of income subject to the higher marginal rate is, well, marginal, part 3 seems somewhat less important than part 2. The real issue is whether the capital gains rate hits the entire profit, since, in that case, it seems the household should only sell enough stock to generate a $9000 profit, and sell the remainder in a future year. How to prove the property of the Lemoine point of a triangle? From Wolfram , I know there is a Lemoine point of triangle, also called symmedian point, the sum of squared distances of this point to all the three sides is algebraically minimum.    How to prove such a property? 18.04 ctrl+shift to change language Daily Ubuntu base update I am getting Ubuntu base update almost every day. This seems strange to me. What am I missing?   (I am using Ubuntu 14.04 LTS) What is a word that means "someone who pretends to be your friend but is actually your enemy?" How should I setup separate MX records for a subdomain? Let's say I have a domain that I run a web application on, for example cranketywidgets.com, and I'm using  for handling email for people working on that domain, for example, support@ cranketywidgets.com, jane@cranketywidgets.com, joe@cranketywidgets.com and so on.  Google's own mail services aren't always the best for sending automated reminder emails, comment notifications and so on, so the current solution I plan to pursue is to create a separate subdomain called mailer.cranketywidgets.com, run a mail server off it, and create a few accounts specifically for sending these kinds of emails.  What should the MX records and A records look like here for this?  I'm somewhat confused by the fact that MX records can be names, but that they must eventually resolve to an A record. What should the records look like here?  cranketywidgets.com - A record to actual server like 10.24.233.214  cranketywidgets.com - MX records for Google's email applications  mailer.cranketywidgets.com - MX name pointing to server's IP address  I would greatly appeciate some help on this - the answer seems like it'll be obvious, but email spam is a difficult problem to solve. I just attempted to fix a typo on a question on cooking.stackexchange.com and saw this     Oops! Your edit couldn't be submitted because:         Your edit summary must be at least 10 characters   This edit is less than 6 characters; surely more can be improved with your edit?      So, misspelled words have to just be left misspelled?  That could prevent the post from being found in a search. How does entropy depend on location and scale? How can I get CSS comments with jQuery? I am wondering how I can read CSS comments out of a linked stylesheet.  I have this sample CSS loaded via:  &lt;link rel="stylesheet" type="text/css" media="all" href="test.css" /&gt;   &nbsp;  #test1{ border:1px solid #000; } #test2{ border:1px solid #000; } #test3{/* sample comment text I'm trying to read */}   I'm testing this in FF3. The following javascript reads the rules but doesn't read the comments in#test3.  window.onload = function(){     s=document.styleSheets;     for(i=0;i &lt; s[0].cssRules.length;i++){         alert(s[0].cssRules[i].cssText);     } } Is it possible to backup individual files with Deja Dup? In the Deja Dup preferences, it is possible to select certain folders to backup and certain folders to exclude.  I would like to be able to backup individual files in my Home folder (Such as .vimrc and .bashrc), but I don't see any way to do this.   So my question is, is it possible to either     Select individual files (instead of whole folders) to backup, or backup my Home folder, but exclude all subfolders? 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Book about space alien cats I read a book when I was young, it was about space alien cats. I believe the title was Quzzles, but I really don't know. The book was stolen from me before I was finished. I don't know much else about it. Define a relation and find its equivalence classes. Word for two collections that do not have any elements in common How do you concatenate characters in java? Concatenating strings would only require a + between the strings, but concatenating chars using + will change the value of the char into ascii and hence giving a numerical output. I want to do System.out.println(char1+char2+char3... and create a String word like this.  I could do   System.out.print(char1); System.out.print(char2); System.out.print(char3);   But, this will only get me the characters in 1 line. I need it as a string. Any help would be appreciated.  Thanks Offset a background image from the right using CSS Double dispatch in C#?