I'll respond until I pass out in a drunken stupor and then get back to you in the morning.
I absolutely would do that if I could, but unfortunately due to the circumstances of a bizzare time warp.
As I was finishing my equations and about to take a picture to share with you.
A bizzare disheveled younger looking version of myself came through a strange portal
yelling something about he's from 2020 and needs something to wipe his ass with.
I don't recall this which makes something of a paradox in itself. But he was also holding a half empty bottle of rum...... So I can't rule out that this happend.
Anyways. I'm too traumatized from that expiernece to recreate my equations. I do apologize though.
That particular problem sounds pretty trivial and could just be left to the interested reader. I'm sure no organizations would be interested if anybody could provide you and answer to that.
How can you prove whether or not, for all problems for which an algorithm can verify a given solution quickly (i.e., in polynomial time), an algorithm can also find that solution quickly?