Is the ideal generated by the set $\{2,x\}$ in $\mathbb Z[x]$ a Principal Ideal?
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
I am getting FATAL_ERROR|System.QueryException: List has no rows for assignment to SObject. I know that it is because it is not returning any rows in the SOQL query but what I want is that if it returns any row, it should update ALO field on contact object, if it is null then ALO field should be set to null.  Here is my code:  ziptoLOD = [SELECT Id, Name, LOD__c             FROM Zip_3_to_LOD__c             WHERE Name =: contact.Extract_Zipcode__c ];  Zip_3_to_LOD__c ziptoLOD2 = (ziptoLOD != null) ? ziptoLOD : null;  if (ziptoLOD2 == null) {     contact.ALO__c = ' ';    } else {     System.debug(System.LoggingLevel.ERROR, 'Zip to LOD' + ziptoLOD2);     contact.ALO__c = ziptoLOD2.LOD__c; }   My code gets stuck at the SOQL query and gives me the list has no rows error. I am trying to help my daughter on her math homework and I am having some trouble on some equation solving steps. My current major concern relies on understanding why $\sqrt{8}/2$ equal to $\sqrt{2}$.  Thanks in advance Order of an element in a finite cyclic group How to reinstall Ubuntu keeping my data intact? I want to reinstall Ubuntu keeping my data intact. I have 160 GB hardrive (sata or pata I don't know but it's slim and made in China) with a 40 GB ext3 partition, a 4GB swap memory and 3 other partition with a FAT32 file system. I have around 4GB space on my drive where Linux is installed.  I'd like to keep the data intact, especially the Downloads folder, desktop, and /var/www; And I no longer have access to any other machines or external storage devices. How can I remove these apps from my device? Literal @YES not working in iOS 5 / Xcode 4.4 How to map inherited entities in EF code-first Command line move file with long directory path without repeating directory path Is there any way of executing a mv command without typing the full path in the second argument?  Example:  mv my/file/that/has/a/really/long/path/foo.bar some_magic_operator_that_means_the_same_directory/foo.baz Suppose you have a group isomorphism given by the first isomorphism theorem: $$G/\ker(\phi) \simeq \operatorname{im}(\phi)$$ What can we say about the group $\ker(\phi)\times \operatorname{im}(\phi)$? In particular, when does the following hold: $$G\simeq \ker(\phi)\times \operatorname{im}(\phi)?$$ I ask this question because i want to prove that $GL_n^+(\mathbb{R}) \simeq SL_n(\mathbb{R}) \times \mathbb{R}^*_{&gt;0}$, with $GL_n^+(\mathbb{R})$ the group of matrices with positive determinant. I proved that $SL_n(\mathbb{R})$ is a normal subgroup and that $GL_n^+(\mathbb{R})/  SL_n(\mathbb{R}) \simeq \mathbb{R}^*_{&gt;0}$, using the surjective homomorphism $\det(M)$. I tried something with semidirect products but I got stuck. I checked this  but didn't fully understand it.   I know that the volume of a right circular cone is $V = \frac{1}{3}\pi x^2h$  I know that I must take the first derivative and set it equal to zero, which will find the maximum.   My problem is how to deal with the variable $h$, the height?   How can I rewrite that in terms of $x$ or $r$.      I have tried to implicitly differentiate this equation, but that wasn't helpful for me. Let   consider   a  square $10\times 10$   and  write  in  the   every   unit  square    the   numbers   from  $1$  to  $100$   such  that   every  two   consecutive  numbers  are  in   squares   which  has  a  common edge.  Then  there  are  two  perfect  squares   on  the  same line  or  column. Can  you   give  me  an  hint? How  to  start? How do I get lightning:datatable to do some undocumented thing X? bi-directional sync with rsync Share Wireless connection with Wired Ethernet Port Is there a way to have a 64 bit enum in C++?  Whilst refactoring some code I came across bunch of #defines which would be better as an enum, but being greater than 32 bit causes the compiler to error.  For some reason I thought the following might work:  enum MY_ENUM : unsigned __int64   {       LARGE_VALUE = 0x1000000000000000,   }; I know this, but I can't recollect at all.   What is this thing called?   They are usually centered in a book or writing and I'm certain they have a name but I can't remember for the life of me. They also come in all shapes, colors and sizes. ggplot2: facet_wrap strip color based on variable in data set I'm using the ieee style for biblatex and when inserting citations I want     [1,2,6-10]   Right now I'm getting     [1],[2],[6-10].   How can I change this? I think the questions says it all! :)  By TeX, I mean any derivative of TeX as long as the code is clearly a derivative of TeX, i.e. that it could belong on TeX.SX (and not pure Lua for example).  I'll give two answers myself so you see what I mean. A Good Book for Mathematical Probability Theory