Yeah, as you've seen, I'm not limited to just one upvote; sometimes different people solve different parts of the puzzle.
I quite like this question :-) Without many stated conditions, the nature of integer arithmetic is enough to really narrow down the field!
The odd-and-even argument is good; one extra insight about the geometry of the rectangles.
And... everyone else is free to join in!
Yes, I've seen that. It was more kind of a personal thing with motivation and so.
So if I see an unsolved or not completly solved question I'm more likely to give the highes effort possible. Anyway now I've time to try finishing it. Thanks by the way for posting all these interesting questions and also for upvoting. Much appreciated!
If I don't get it today I'll probably ask my mother, if she also wants to try. She's a math teacher in Grundschule (elementary school) and also quite enjoys mathematical questions, riddles or similar things.