A decent start? It says absolutely nothing about how to solve it, except repeating the question. The part where it tries out the few first numbers is entirely wrong, given that 6 does _not_ satisfy the condition (2 does not divide 3+6=9) and 8 _does_ (2 does divide 4+8=12).
Amusingly, the list of the integers Given that GPT4 is not a model but a full product, behind the scenes it probably coded up and ran a small python code that translated the problem into code, executed it and got its solution for the first few integers. Which would be a good thing to do to start solving a problem like this, except you're not allowed to do that at the IMO, obviously.
Looking at the output of this program, it suggests that powers of primes could be a class of solution (or maybe even the only solutions? I guess that's all the problem was _really_ asking to prove, but having never qualified for the IMO myself, I can't be sure). In fact, for n = p^k, the divisors are [1, p, p^2, ..., p^{k-1}, p^k], and clearly always p^i divides p^{i+1} + p^{i+2} = p^i (p + p^2). I guess this small remark would have gained me a point at the IMO, only 41 to go ;-)
But the other side of the coin is that having those numbers written down in front of you and not even making a conjecture about powers of prime being the answer would really denote poor mathematical reasoning by GPT4. It's only really proving that it can understand what it's being asked, which, I admit, places it in a better position than maybe 90% of the human population, but unfortunately for GPT4 mathematics is the least democratic science of them all - it's always only the top-1 result that matters in the end.
P.S. Being a former mathematician currently working on deep learning, having (or building!) a model that can solve mathematical questions has always been my dream. I'm not even talking about something that can _prove_ things, even just that can understand and rephrase them in different settings (which in mathematics is very, very hard, even for a human). Or spot weaknesses in already stated down proofs. As a graduate student, having something I could chat about to ask silly question while studying a paper would have been a real game changer. Even for best-of-world professionals it would be useful: when the wrong proof about the ABC conjecture came out, it took months of work from the best minds of our world to read through it and disprove it. If Mochizuki had had some tool for automatically checking his proof (and a smaller ego, I guess) he could have caught that early on, saved everybody a lot of work and the whole world some useless drama.
And while we're closer than ever to reaching that, I think GPT4 is still quite a far way from it. But with the pace we've seen recently in AI evolution, who knows...