Given a polynomial f(x₁,x₂,...,x_t) in t variables with integer coefficients and a positive integer n, let α(n) be the number of integers 0 ≤ a < n such that the polynomial congruence f(x₁,x₂, ...,x_t) ≡ a (mod n) is solvable. We describe a method that allows us to determine the function α associated with polynomials of the form c₁x^k₁ + c₂x^k₂ + ··· + c_tx^k_t. Then, we apply this method to polynomials that involve sums and differences of squares, mainly to the polynomials x² + y², x² − y², and x² + y² + z².