Theorem 1 - part 1

DynV · #1 $Old$ October 20th, 2009, 10:27 AM

I've seen pretty much the same description at the page A theorem of number theory.

I'm having trouble understanding that theorem ; the first examples that comes to mind is a=12, b=3, b=4 so that none of the parts make sense to me.

I also don't get the proof of the first part as to me a should be bigger than b or c so that s and t should be a fraction (ie: 2/3), not an integer.

I'm really stuck there and in a rush preparing for an exam
Thank you kindly for your help

TheEmptySet · #2 $Old$ October 20th, 2009, 11:51 AM

I think you may misunderstand the notation.

$a|b$ means that $\frac{b}{a}$ is an integer. i.e there is an integer k such that $a \cdot k =b$

DynV · #3 $Old$ October 20th, 2009, 12:46 PM

Quote:

Originally Posted by TheEmptySet $View Post$

I think you may misunderstand the notation.

$a|b$ means that $\frac{b}{a}$ is an integer. i.e there is an integer k such that $a \cdot k =b$

I now see that TheEmptySet was right.

I was seeing it reversed and made no sense. I knew the chance of having such an important error in a book revised 3 times by numerous important people was quite unlikely but wasn't understanding why. I though I was going to have to learn that section by heart ...

Thanks