@VaclavKotesovec: Can you get a look at this question: math.stackexchange.com/questions/4354098/… because Gerry Myerson gives a link to one of your works.

@JoshuaZ: But the problem is to find an equation that is unsolvable.

@Wojowu: Can you explain to me in few words how one can find that equation.

@AndrésE.Caicedo: I have a nonlinear diophantine equation of the form $$f(x,y,z,t)=g(x)t+h(x,y)z+w(x,y)=0$$ Then I am asking if one can consider this equation as a linear one in $t$ and $z$ and apply the same methods known for linear equations with $2$ variables.

@GHfromMO; What about the polynomials with several variables and irreducible over the set of integers.

What about the polynomials with several variables and irreducible over the set of integers.