I'm having a hard time with this proof:

Show that if a and b are positive integers then

Thanks everyone!

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- Nov 15th 2009, 08:46 AMrubik maniaHelp with proof with greatest integer function
I'm having a hard time with this proof:

Show that if a and b are positive integers then

Thanks everyone! - Nov 15th 2009, 07:03 PMhatsoff
- Nov 15th 2009, 07:25 PMrubik mania
Sorry, I forgot to mention:[x] is the greatest integer function.

so

, so it actually works. - Nov 17th 2009, 05:04 PMrubik mania
ok, this is what I have so far...

Let be the set of all pairs of integers (x,y) satisfying

The set has members

Separate into subsets , according as

The set can be described as the set of all pairs (x,y) such that

The number of pairs in is then seen to be

Similarly, consists of the pairs of (x,y) such that

and the number of pairs in is

Now this is where I am still stuck on:

somehow, when you account for , there may be a third set, that is somehow equivalent to number of elements total. How do you show that this is true?