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## anonymous 5 years ago I am studying Diophantine equations, and I don't understand the underlined portion of my attachment. (Attached in my next post)

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1. anonymous

Here is my attachment. Please help.

2. anonymous

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

3. anonymous

Hello.

4. anonymous

Hello, did you decide to abandon me? :)

5. anonymous

??

6. anonymous

Remember you promised to look into those problems in this weekend

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

Do you want the answer to this one? ;)

11. anonymous

Or have you figured it out already?

12. anonymous

Yes ofcourse,

13. anonymous

Is that a thing to ask? :)

14. anonymous

No I haven't figured out anything

15. anonymous

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).

16. anonymous

What an idiot I am

17. anonymous

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 =

18. anonymous

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

19. anonymous

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

20. anonymous

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

21. anonymous

I mean it is simple enough

22. anonymous

And I shouldn't have asked it

23. anonymous

Anyhow thanks thanks thanks thanks both of you

24. anonymous

yw

25. anonymous

np :)

26. anonymous

Anyhow - I need sleep.

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