Squarefree values of multivariable polynomials

Given f (element of) Z[x1, .... , xn], we compute the density of x (element) Z^n such that f(x) is squarefree, assuming the abcconjecture. Given f,g (element of) Z[x1, .... , xn] , we compute unconditionally the density of x (element) Z^n such that gcd(f(x)< g (x))=1. Function field analogues of both results are proved unconditionally. Finally, assuming the abc-conjecture, given f (element of) Z[x], we estimate the size of the image of f ({1,2,...,n}) in (Q^*/Q^*2) (intersection) [Q].