There don’t seem to be any small ones. Perfect cuboids would be examples, so a proof that no examples exist that are not perfect cuboids would also be very interesting.
1
-
$\begingroup$ The perfect cuboid problem is hard enough, a different sounding problem is unlikely to be easier. Indeed, the (non) existence of perfect cuboids is related to the Bombieri-Lang conjecture, so a proof of non-existence (or even just finitely many) perfect cuboids would amount to proving a case of Bombieri-Lang, which would be a huge accomplishment. $\endgroup$– Stanley Yao XiaoCommented Oct 15, 2023 at 18:29
Add a comment
|