I have been playing around with diophantine equations after watching Numberphiles video on the “uncracked problem of 33”
A related equation is discussed here https://arxiv.org/abs/1109.2396 and here http://www.asahi-net.or.jp/~kc2h-msm/mathland/math04/cube02.htm
Playing with different methods for searching for solutions, I have come up with a new one for the previous unsolved d=2372 as can be verified in python:
-16870920115 ^ 3 + 3384145055 ^ 3 + 2 * 13354335746 ^ 3 2372L
(edit: had to change double asterix to hat because reddit formatting )
What should I do about this? I have tried contacting the author of the ArchiveX paper, for advice, without success.
I just recently learned about the yoneda lemma and I have this question: If we look at a arbitrary functor F in [C,Set] and we see that F a (where a is an object in C) is not the empty set, does that imply that there is a natural transformation from the homefunctor C(a,_) to F? And does that mean that the functor F is representable?