If you add up inverses of odd numbers, can you get an even integer? Of course, I mean you only use each odd integer once... so 1/3 * 6 doesn't work. I remember seeming to think that if this could be proved impossible, one could provide an elementary proof of Fermat's last theorem. Undoubtedly false then as it is now, but... Thoughts? Is this a rabbit hole? Or can you prove / disprove the adding up inverses of odd integers thing?