I'm having a hard time with this proof:
Show that if a and b are positive integers then
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?