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 Feb9 awarded Nice Answer Jun21 awarded Yearling Jan21 revised Is it possible to prove a mathematical statement by proving that a proof exists? Fix incorrect argument related to the characteristic of the field Jan18 comment Is it possible to prove a mathematical statement by proving that a proof exists? Rudin's proof seems more powerful than the model-theory proof above, and it elucidates better why the theorem is true. Still, this is a standard proof which directly addresses the original question. Jan18 comment Is it possible to prove a mathematical statement by proving that a proof exists? Not off the top of my head. I'm guessing it goes something like this: Since every function on finite fields is a polynomial function, there should be an upper bound $U(n, d, p)$ on the degree of the inverse for every $n$. If that function can be made independent of $p$, then just use "$\phi_{d,n}$ AND there is a polynomial of degree at most $U(n,d)$ which is an inverse of $f$" instead of just $\phi_{d,n}$. The proof would go the same. I don't know how to make the upper bound on the degree independent of $p$, however. (Is it possible?) Jan18 revised Is it possible to prove a mathematical statement by proving that a proof exists? Clean up sentence. Jan18 awarded Editor Jan18 revised Is it possible to prove a mathematical statement by proving that a proof exists? Improve confusing choice of variable name. Jan18 answered Is it possible to prove a mathematical statement by proving that a proof exists? Jan11 awarded Teacher Jan11 answered How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards? Jan11 awarded Supporter Jun21 awarded Autobiographer