This particular question is a part of an assignment which could not be discussed due to pandemic .
Question (a) Consider the ring R of polynomials in n variables with integer coefficients . Prove that the polynomial $f(x_1 , x_2 ,\ldots, x_n) = x_1 x_2\cdots x_n $ has $2^{n+1}-2$ non-constant polynomials in R dividing it .
Attempt: (a) any polynomial in R dividing f would be of form ${x_{1}}^{i} ...{x_{n}}^{i}$ i=0 or 1. So , there will be $2^{n}-1$ polynomials . But the answer is 2 times my answer.
Thanks!!