Sum of nil left ideals
Sum of nil right ideals
The equation $y^2 = x^3 + k$ for $k = (4n-1)^3 - 4m^2$, with $m, n \in \mathbb{N}$ and no prime number that p is congruent to 1 modulo 4 divids m, doesn't have any answer and its proof can be obtained by using quadratic reciprocity law.  Do you know answers of this equation for two or three different values of $k$? In addition, do you know any reference about that? Can you use an alias in the WHERE clause in mysql? I need to use an alias in the WHERE clause, but It keeps telling me that its an unknown column. Is there any way to get around this issue? I need to select records that have a rating higher than x. Rating is calculated as the following alias:  sum(reviews.rev_rating)/count(reviews.rev_id) as avg_rating When writing answers on here, it's often necessary to create a new script and chmod +x it to make it executable. I won't go into whether this is a good thing or not, but explaining to people that they need to fire in three separate command (and teaching them to use nano!) is a bit of a waffle.  Is there anything easier? Is it safe to fully cook a stuffed turkey the night before thanksgiving? Let  $$0 \rightarrow M \rightarrow N \rightarrow P \rightarrow 0$$  be an exact sequence of $A$-modules, where $A$ is a commutative ring with unity.  Then for each natural number $i$ one can look at the induced maps  $$\mathrm{Sym}^i(N) \rightarrow \mathrm{Sym}^i(P)$$  and   $$\mathrm{Sym}^i(M) \rightarrow \mathrm{Sym}^i(N).$$  The first question is, if they are still surjective, resp. injective, i.e. is $\mathrm{Sym}^i$ an exact functor?  The second question is: what are the kernel, resp. cokernel of these maps? Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible On the nilpotence of the matrix $AB-BA$ Windows 8 upgrade Recovery Disk I have upgraded to Windows 8 from Win 7. I want to create a recovery disk for Windows 8, just in case something goes wrong. I didn't find the option of creating it from the control panel.  How do I create a Recovery CD/DVD? Generate mesh at run time Is it possible to generate mesh at runtime in blender game engine? That is, is it possible for blender to generate meshes using python code when the game runs?  I really would like to know if this is possible, as my final year project requires use of this. Normal subgroup of prime index Generalizing the case $p=2$ we would like to know if the statement below is true.  Let $p$ the smallest prime dividing the order of $G$. If $H$ is a subgroup of $G$ with index $p$ then $H$ is normal. What's a good Windows RDP client for Mac? I administer a number of Windows machines, and am trying to find a really good application to remote desktop in to them from my Mac.  I've tried CoRD, and I really like its library approach to saved sessions (as opposed to Microsoft's file based approach), and tabbed sessions are great when working on a bunch of machines.  Unfortunately, it's just too buggy for serious use, and given that it averages less than 2 releases a year, I have little hope that that will change.  Microsoft's official client is very bare bones and doesn't support connecting on non-standard ports (which I need).  Is there a remote desktop client for Mac out there that's both fully featured and not buggy?  Edit: Apparently the Microsoft doc I read that states that the Microsoft RDC client can't be used on non-standard ports is out of date. Where did Hogwarts get money for salaries, food and other purchases? Semicolons at the end of list items In school, we were taught to end each list item with a semicolon. But I have never actually seen this. Can somebody please confirm this? Should we end each list item with anything at all?  I've seen people use periods after each list item, colons, and even commas. But I've never seen a semicolon at the end of each item — and even if I have, it would be that rare that I've forgotten.  Example:   item; item; item; item Frobenius Inequality Rank I was looking for an answer for this problem in terms of matrices, but I really don't know how to prove this result. The proposition says that:  Let $A\in M_{m\times k}(\mathbb{C})$, $B\in M_{k\times p}(\mathbb{C})$ and $C\in M_{p\times n}(\mathbb{C})$, then $\textrm{rank}(AB)+\textrm{rank}(BC)\leq \textrm{rank}(B)+\textrm{rank}(ABC)$ bash function cannot change the value of a local variable when called by $() The following code works differently depending on which way Parse_Short_Switches() is called.  After calling the function 'Parse_Short_Switches' by using result=$(Parse_Short_Switches), the value of $error_flag is NOT set to -1 as I would expect.  After calling the function 'Parse_Short_Switches' by simply using Parse_Short_Switches, the the value of $error_flag is set to -1 as I would expect.  Any help would be greatly appreciated.  Thanks  #!/bin/bash  function Parse_Short_Switches() { echo "error_flag inside of the function= $error_flag" 1&gt;&amp;2 error_flag="-1" echo "blah blah ..." }  # --- MAIN --- error_flag="999" echo "error_flag= $error_flag" #result=$(Parse_Short_Switches) Parse_Short_Switches echo "error_flag= $error_flag" How to combine various armatures? Can we use an Android phone as a Wi-Fi repeater? Can we use an Android phone as a Wi-Fi repeater?  Imagine situation when you can access a weak Wi-Fi signal from a free hotspot (coffee shop) signal near window, but want to work in the middle of the room. 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Python's lists, [1, 2, 3, 4, 5], and tuples, (1, 2, 3, 4, 5), are not, in fact, linked lists, and linked lists have some nice properties such as constant-time concatenation, and being able to reference separate parts of them. Make them immutable and they are really easy to work with!