This answer here: https://math.stackexchange.com/a/1083253/1102
I flagged it as 'not an answer', as it ought to be a comment, but the flag was
declined disputed. I believe there were a few delete votes on it too, not sure what happened to those.
It is fine to be skeptical about inequalities like this (even I am), but apparently this is a contest problem, so such 'answers' are unwarranted.
Even if it was not a contest problem, this is still a comment.
Why are the moderators encouraging such non-answers?