Re: Number theory puzzle

On May 8, 8:43 pm, "Larry Hammick" <larryhamm...@xxxxxxxxx> wrote:
Let p and q be positive relatively prime odd, say
p = 2a + 1
q = 2b + 1.
Let k be the number of pairs (x,y) of integers such that
1 <= x
1 <= y
2(xp + yq) < pq.
Show that ab-k is an even number.

"Eigenray" has posted a solution.
http://www.mathlinks.ro/Forum/viewtopic.php?t=148026

Here at the Sortov Institute we invested quite a bit of midnight oil
in this proposition, eventually getting a proof in terms of
permutations. It's longer but a little more "elementary" than
Eigenray's proof.

.