Question

I am studying Diophantine equations, and I don't understand the underlined portion of my attachment. (Attached in my next post)

Answer 1

Here is my attachment. Please help.

Answer 2

change q back into b/d and see what happens?

Answer 3

Hello.

Answer 4

Hello, did you decide to abandon me? :)

Answer 5

??

Answer 6

Remember you promised to look into those problems in this weekend

Answer 7

Oh - I have been preoccupied. I'll look tomorrow. I can help you with this one now, though.

Answer 8

I thought I did something wrong, perhaps said something I shouldn't have said, or something of that sort.

Answer 9

No, you need to calm down :) I keep saying that.

Answer 10

Do you want the answer to this one? ;)

Answer 11

Or have you figured it out already?

Answer 12

Yes ofcourse,

Answer 13

Is that a thing to ask? :)

Answer 14

No I haven't figured out anything

Answer 15

Okay...look at the equation you get,\[p(x-x_0)+q(y-y_0)=0\]then\[(y-y_0)=-\frac{p(x-x_0)}{q}\]The left-hand side is an integer, and you're told that p and q are relatively prime, so for the right-hand side to remain an integer, it must be that q divides (x-x_0).

Answer 16

What an idiot I am

Answer 17

a(x-x0)+b(y-y0)=0

b(x-x0) = -a(y-y0)

b/d=q; a/d=p

q(y-y0) = -p(x-x0)

(y-y0) = -p (x-x0)/q

y-y0 =

Answer 18

Thinking over this for the last 1 hour but didn't figure this thing out

Answer 19

Just keep thinking of NUMBERS. These equations are about NUMBERS.

Answer 20

Yeah, I understand it now. Infact as I told, I should have figured this thing myself. But couldn't

Answer 21

I mean it is simple enough

Answer 22

And I shouldn't have asked it

Answer 23

Anyhow thanks thanks thanks thanks both of you

Answer 24

yw

Answer 25

np :)

Answer 26

Anyhow - I need sleep.