I wonder, is there a relationship between P!=NP and Hilbert's 10th problem? It seems to me that P!=NP is pretty much saying that integer solutions for certain c

I wonder, is there a relationship between P!=NP and Hilbert's 10th problem? It seems to me that P!=NP is pretty much saying that integer solutions for certain class of polynomials are easy to check (once you have them) but hard to describe as a set (there isn't always a representation with the polynomial algorithm), but I don't know how to put it formally.