A2 is equally flawed. It gives the right solution, and a proof for n=1 but for n=>2 it basically bails out with "it's much harder to achieve a neat identity". So again, if the test requires a proof for the solution, this is definitely not it.

For those that heard that o1 aced the Putnam test, well - no, it did not. For A1 it does demonstrate that n=1 has infinite solutions and that n=2 has no solution, but gives no real demonstration for n>2. It would probably not score as a valid pass.

I am testing QwQ-32B (using this quantized version: huggingface.co/sbeltz/QwQ-3... ) on my lowly AMD device. Oh boy, does it perform. It is very, very chatty, takes a looong time to think, but it reaches the right answer at the end.