I guess the confidence comes from having tried it with a bunch of numbers. I'm sure there are people that have written programs that just tried to show the iden

I guess the confidence comes from having tried it with a bunch of numbers. I'm sure there are people that have written programs that just tried to show the identity holds for all numbers up to n with n very large. Of course the problem is you can't show this by exhaustion. And you also can't currently prove it, hence why its a conjecture. But it's interesting because it means you might be missing some integral property that would prove the conjecture.