discrete math help
 

I need some help from our resident math genius posters. I am working on my discrete stuff and I need help with the following problem

find the gcd of a = -1575 and b = 231, write it in the form alphaX + betab, where alpha , B belong to Z.

we were taught a method like this

-1575 1 0
231 0 1

then find q ( a/b floored if b>o and take the ceiling if b<0)
then r which is : a-qb

and then that makes the next row with the numbers under the 0 and 1 are found by such (1-q(0), and 0-q(1)... the 1 in the first part is from the first row second column and the zero is from the second row second column) Then same idea for the next number. and that method is used down the line.

its hard to explain I guess... I need to do good on this homework so it helps my grade. If anything I can scan in the sheet.

if you know what I am talking about let me know what you get. I just worked through it slowly, double checking my method and I got, in the proper form

gcd(-1575,231) = -21 = 5(-1575)+34(231)

5(-1575)+34(231) = -21

so I guess it checks out?

certainly not a math genius... but what is the name of the process you are supposed to be learning (ie.. chapter name etc..)? There are a few ways to do this.

Perhaps you can teach us... thats the best way to learn.

Anytime you are writing anything and are going to use abbreviations you need to spell out what that is the first time ... then you can use the shortened version and people will know what you are referring to..
Not just here... but that is standard practice in English for all writing.

I got the same using Euclid. Nice job.

Can GCD's be negative?

good catch, buddy.

it shouldn't be.

OP: in the first step, take a -1 out of -1575 to make it (-1)1575 and bring that over so that you get 1575=6*231+189 and carry it through your work.

you could just switch the signs at the end, but it depends on your teacher and how you see it.

21=-5(-1575)-34(231)

Euclids method is one way then we learned this other way which I have no idea of the name. But apparently I did it correctly.

Are you row-reducing or using a determinant?

You saw Yak's post right?

Someone needs to share with the lower math people what yall are talking about...

GCD = greatest common denominator.

21 is the largest number that goes into both 1575 (or -1575) and 231.

There are different methods. Euclidean and Matrix are two.

If the teacher expects a linear equation, then your coefficients (alpha and beta) may have the wrong sign and you won't get max points.

I'd review your notes or examples and see if there's anything about "ignore the minus sign".

I thought that was ' Great Carbon Diode '....
so we are just talking finding largest common factors ?

I disagree. WGAS at our advanced ages. Art history, music, language, I can see, but math? I am checking out of this one....

Maybe row reducing. With negative number it was not an issue since it did work out. Maybe I'll scan inmy work later and show you all.

Here is another one for you all

Prove that the equation 3X ≡ 1 mod 6 has no solutions.

so far I have it solved for x which is x = 2k - 1/3 and then I am stuck

I honestly need help with all of it. I have posted a screen cap of the page this is on.

page 1
http://i3.photobucket.com/albums/y74...24/page2-1.jpg

page 2
http://i3.photobucket.com/albums/y74...rx24/page2.jpg