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Ok so I'm stuck on this one problem.

Let a,b,c be nonzero integers. Show that gcd(a,b) = 1 and gcd(a,c)=1 if and only if gcd(a,lcm[b,c]) =1.

I tried converting gcd(a,b) into a linear combination, with no luck. I also tried using the corollary gcd(a,b)*lcm[a,b]=ab, also with no luck. Any help on this would be appreciated.

So I haven't a clue how to do this. I don't even know how to direct sum two things, regardless of what the theorem says. How can they be approximately equal to (perhaps congruent, but the symbol is clearly approximately equal to). I understand that Z is integers, but what does Zn represent?

I am trying to traverse a folder and all of its directories and copy the files up to the previous folder. For example, my main folder is

C:Music

Within the music folder is a folder with all of the artists, like this:

C:Music\Artist

Within the Artist folders are more folders with the name of the albums, something like this:

C:Music\Artist\Album\files.mp3

I have a radio in my car that can play music off of a flash drive but only supports 500 total folders. Therefore I want to copy all of the files from C:Music\Artist\Album into C:Music\Artist and delete the album folder. The only problem is I cannot find the command to go to the next folder within a directory using a batch file so that I can do the same process for all albums in every artist folder.

I have been unable to get usb support to work in virtualbox. I add the filter for the device I want to use. Once I go to attach it to the virtual machine I always get the message that says "failed to attach the usb device...is busy with a previous request." I have tried empty filters, I have tried to change the settings, everything I can think of. The host OS is Vista Home Premium and the guest is XP Pro.

The copy of Microsoft Office 2007 will allow me to install it on 3 computers, and I already have it installed on 3. When the program is registered, Microsoft keeps a record of what computers it is installed on because you have to activate it either by phone or through the internet. I just bought a new computer and want to install it. If I uninstall it on my old computer will it recognize it as being uninstalled on Microsoft's end and allow me to install it on my new computer?

I need to use the dos function ah=2a to get the current date of my machine. I type debug under the command prompt and then I do the following:

-a 100

137A:0100 mov ah,2a

137A:0102 int 21

137A:0104 ret

137A:0105

-g 100

Program terminated normally

-r

This will display the registers, and supposedly the year will be in cx, the month in dh, the day of month in dl and day of week in al after using the dos function ah=2a. However, all of them are zero, so it seems that the program does nothing. What did I do wrong?

I need to verify input using cin in c++. Essentially, I need to make sure that if I am asking for an integer the user actually entered an integer before I continue with my code. For example:

int number;

cout << "Please enter an integer: ";

cin >> number; //number may or may not be an integer after using cin

I cannot find any way in which to be sure that what they input was an integer I have tried it with loops and cin.ignore(), cin.clear() but nothing seems to work. Basically, I want to check if they entered an integer, and if they didn't output a message saying that invalid data was entered and prompt for them to re-enter it. I am experienced in java and this is extremely easy to do, however it seems that there is no easy way to do this in c++.

I think the backup partition on my friends' computer is corrupted (it won't restore the computer to the original state from there). If I delete the partition and insert the compaq recovery discs, will it recreate the backup partition?

My friends' computer would boot up and log in, but merely seconds after logging in the computer would just simply shut off for no reason. I told her it was probably a virus and a fresh installation of Windows XP was probably her best bet. Before I tried reinstalling windows I tried the system recovery tool that compaq supplied, but the computer suddenly shut off and corrupted a few dll files, and now her computer won't boot at all. So I tried to do a complete reinstall of Windows, but it would get to a certain point and then it said it cannot copy certain dll files, and asked me to retry or skip...retrying didn't work, and after skipping a few the computer would just shut off. The latest error it gave was memory management. I even tried deleting the partition before installing windows, with no luck. Is it possible the recovery partition is causing problems? I also read the RAM may be faulty, I'm going to run a program to test the RAM. Or maybe the hard drive is bad? Or the cd?

I understand how to prove things with induction (I took a discrete course in college) however this is not your typical induction... How do I prove that the derivatives of any order are linear by induction?

I don't know about you guys, but it seems as though the media is assuming that Hillary Clinton or another democrat is going to become the next president. They have given almost no time to anyone else; it's Hillary this, Hillary that, over and over again. What about the rest of the candidates? Rarely do I hear them talk about a Republican candidate and definitely not an Independent candidate. What's worse is that people are going to vote in a Democrat because that is all they are hearing about. To complicate matters, people are going to vote for a Democrat not because they think a Democrat is the best candidate, but because George Bush is a Republican, so they assume all Republicans will run the country like Mr. Bush. For those of you who are actually educated on the issues and decide that a Democratic candidate is the best, then by all means vote for one. But don't do it because of the media or because of President Bush.

I need a word that means "the person who is being talked about in a poem or short story". In the poems I read, the two people are talking about their death after they died, and I need a good word to describe who these people are.

Is $1500 a reasonable price for an 01 Arctic Cat 370 snowmobile with 950 miles on it? It is not from a dealer, but from a private seller. It started right up and doesn't seem to have anything wrong with it other than a cracked seat.

I need to generate a list of random numbers (sat scores in particular). There is a random number generator in excel that generates random numbers in a normal distribution, but I can't find a way to have it generate random integers that go from 200 to 800; only numbers with decimals that go from any value to any value.

I am currently a mathematics major with secondary education, however I am going to drop the education aspect of it. I would also like to add in a computer science major or minor. I do not want to drop the math aspect all together, but having two majors would be difficult and require a full schedule. Obviously a minor would require me to take less courses, but does that mean that I wouldn't be able to get a job in the computer science field? Would the pay be less with a minor versus a major? Essentially what I am asking is what are the advantages/disadvantages of a computer science major versus a minor.

This error has just started coming up when I start my computer. I started in safe mode and checked for spyware and viruses, but I had none. Then I ran sfc /scannow to check for missing essential files. However, it asks for a Windows disk, and brand new my computer did not come with one. It did not state which file may be missing. The problem occurs about 2/3 of the time, and it starts up normally 1/3 of the time. Any ideas on finding what file may be missing and how to get it without the cd?

It is an IBM speaker with model number 02K0322. I can't find the AC adapter, so I tried a universal adapter. The adapter had the right voltage but only puts out a maximum of 300 mA. The speakers work very well until I turn the volume up past a certain point, and the quality gets terrible and the green power light flickers. I think that the universal adapter doesn't put out enough mA's to power the speakers at high volumes. Here is what it looks like: http://www.gadgetbee.com/i/IBM02K0322.html

I have had an annoying floater in my eye for nearly five years (I am 19 years old). I was told that nothing could be done about it. After doing some research, I have found a few supposed "cures", which involve certain natural herbs, eye exercises, and even relaxation techniques. Chinese medicine supposedly links floaters to a blocked liver. Are any of these remedies actually going to work, or am I going to have to live with it the rest of my life? Surely there has to be something that can improve it (with replacing the vitreous humor).

Does anyone know the minimum allowable thickness of a 1997 Ford escort brake rotor? I work at a chevy dealership and can cut them myself, but I cannot find out the service information for ford vehicles.

The chair is microfiber. There is super glue on the arm. I've tried acetone, but it didn't work.