Y by Lam.DL.01, Adventure10, Mango247, and 2 other users
Fix two positive integers
, and let
be a nonconstant polynomial. Suppose that for all sufficiently large positive integers
, there exists a rational number
satisfying
. Prove that there exists a polynomial
such that
for all real
.
Victor Wang.

![$f\in\mathbb{Z}[x]$](http://latex.artofproblemsolving.com/1/1/9/119792ece753aa569a509d6f54a0a9f7f9ccc014.png)



![$g\in\mathbb{Q}[x]$](http://latex.artofproblemsolving.com/3/c/c/3cc2b84905c31e9ac10fc0e20791bc725d22c70a.png)


Victor Wang.