What is the smallest particle? What is the building block of an electron?
Do electrons have shape?
Is every sufficiently large positive integer of the form $ab + ac + bc + 1$? Is every sufficiently large positive integer $A$ of the form $ab + ac + bc + 1$   where $a,b,c$ are some positive integers larger than some given positive integer $d$ ?  How large is sufficiently large , in other words how do we know our number $A$ is sufficiently large ( as a function of $d$ ) ?    Update :  I read the following about positive integers that are not of the form $ ab + ac + bc $:    And I quote about that sequence above : " Note that for n in this sequence, n+1 is either a prime, twice a prime, the square of a prime, 8 or 16 "  This is why I considered the weird +1 in $ab + ac + bc + 1$  So composites larger than 16 not a prime , twice a prime or the square of a prime are of the form $ab + ac + bc + 1$.  And I wonder why !  I guess that relates strongly to the Original posted problem. Maybe I should have mentioned that before , sorry.  Will Jagy's answer gave the same OEIS link which I already knew. This also explains some of the comments.  Im no expert in genus theory or Galois theory but I assume this has a simple answer. How exactly do DLL files work? There seems to be an awful lot of them, but I don't know what they are or how they work.  So, what's the deal with them? How can I completely remove ecryptfs from my system and delete .Private? Few days back I have installed ecryptfs, created a private directory using it. Now my Ubuntu login became super slow. I have tried removing ecryptfs from Synaptic. I found It, it can not be deleted that way. Somewhere I have read about this command  ecryptfs-setup-private --undo   But this command displays a rather confusing list of commands on terminal. I don't want to mess up my installation, neither want to loose my administrator account.  Now my question is, how can I safely remove /home/user/Private (.Private) and remove ecryptfs encryption ? Problem: If   $$C_0+\frac{C_1}{2}+\cdots + \frac{C_{n-1}}{n}+\frac{C_n}{n+1} =0,$$  where $C_0,...,C_n$ are real constants, prove that the equation  $$C_0+C_1x+\cdots +C_{n-1}x^{n-1}+C_nx^n=0$$  has at least one real root between $0$ and $1$.  Source: W. Rudin, Principles of Mathematical Analysis, Chapter 5, exercise 4. Inductive proof of the closed formula for the Fibonacci sequence Fibonacci numbers $f(n)$ are defined recursively:  $f(n) = f(n-1) +f(n-2)$ for $n &gt; 2$ and $f(1) = 1$, $f(2) = 1$. They also admit a simple closed form: $$\sqrt 5 f( n ) = \left(\dfrac{1+ \sqrt 5}{2}\right)^n- \left(\dfrac{1 - \sqrt 5}{2}\right)^n \tag1$$  How to prove (1) using induction?  Remarks One could get (1) by the general method of solving recurrences: look for solutions of the form $f(n)=r^n$, then fit them to the initial values. But there should be a more concrete proof for this specific sequence, using the principle of mathematical induction. Why are Flash applications so sluggish/crashy? I've noticed that Flash applications tend to be more sluggish under Ubuntu than they do under Windows on the same machine. This is particularly noticeable when watching HD video or playing graphics/physics-heavy games. Are there any ways of improving the performance of Flash under Ubuntu, or is this just an issue with the Linux version that I will have to live with?  Currently I'm just cutting down on the number of tabs open, blocking flash ads, and closing other programs, but I'm looking for ways to affect Flash itself.  Other things I have already been doing include using Youtube's HTML5 feature and playing videos straight from /tmp in VLC. I was wondering if there was some way of streamlining Flash itself though. Perhaps not.  More Specific Question: Is there anything I can do in mms.cfg to boost performance? Is there a fast way (without looping over all edges/faces/verts) using ops.mesh or bmesh to get the lists of indices associated with mesh islands as shown below? These islands are part of one mesh but are disjoint from each other.    I know how to select the boundaries by running the operator Select boundary Loop or calling bpy.ops.mesh.region_to_loop() but can't find any API calls to return the vert/edge/face indices associated with the individual islands. Kernel requires an x86-64 CPU, but only detected an i686 CPU. How can I install Lubuntu/Ubuntu? I'm trying to install Lubuntu on my laptop (sorta old 2005). [Laptop stats: Intel® Celeron® CPU 410 @ 1.46 GHz 1.47GHz, 448 MB of RAM]  I press Install and this message appears:   This kernel requires an x86-64 CPU, but only detected an i686 CPU.  Unable to boot - please use a kernel appropriate for your CPU.   What can I do to install Lubuntu on my computer? Age replacement policy for hard disks and SSDs at servers I'm planing an age replacement policy for our storage and servers. Most of them are for DBs and some for images (static content) so yes, they have an huge I/O everytime.  Also, we use Samsung 840 Pro SSDs for the RAID Controllers (PERC H700i) as CacheCade.  Are you guys managing the replacement of old hard drives and solid state drives? Do I need a visa for a connecting flight to Japan? I'm going to the Philippines this October and would like to layover in Japan. I found a reasonably priced ticket with a 15-hour layover to Haneda, however, I have to transfer to Narita. Do I need a visa since I'm going to have to stay at a hotel and ride a bus to travel to Narita airport? Thank you! Can I install Windows OS (Windows 7) on a removable USB hard drive? I wanted to take a sneak peek at Windows 7 so I thought of installing it. I have Windows Vista on my laptop which came pre-installed with it. I didn't want to mess with it.  So I created a partition (20 GB) in my USB external hard disk and tried to install Windows 7 on that partition. But when I booted from a Windows 7 DVD and selected the target partition on USB hard disk, it said it cannot be installed.  Is there any way to install Windows on an external USB hard disk? Is there a word which describes terms that are spelled like a particular pronunciation? Some examples: &quot;never&quot; might be written as &quot;neva&quot; &quot;I don't know&quot; is sometimes written as &quot;iono&quot; or &quot;I dunno&quot; on various internet media. My question is: is there a word for this particular technique of spelling a term in the way it is (sometimes) pronounced? Please warn about exceeding 50 question limit prior to asking a new question How do I remove log out, reboot, and shut down from GNOME shell application list? I’m new to Ubuntu. I don't know where the log out, reboot and shut down icons in my application list came from. I just need to remove this from here. Applying for a Canadian ETA after previous visits without one How can I kill the Mirelurk Queen? What's the difference between semicolon and double ampersand && What is the difference between  echo "Hello " ; echo "world"   and  echo "Hello " &amp;&amp; echo "world"   Both seems to run the two commands after each other. How can one link / merge / combine / associate two accounts / users? (Anonymous / unregistered / cookie, or Google / Facebook / registered) How to disable grub menu at boot time in Ubuntu 20.04? Who is blowing the horn to alert the Night's Watch?