I’d appreciate some help regarding this problem.
$x_1, x_2,...,x_n$ are variables $y_1, y_2,...y_{2^n-1}$ are sums of non-empty sunsets of $x_i$
$p_k(x_1, x_2,...,x_n)$ is k-th elementary symmetric polynomial in $y_i$ ( the sum of every product of k distinct $y_i$’s)
For which k and n is every coefficient of $p_k$ even?
After checking some particular cases of k and n its easy to see that in general coefficients are even unless $k= 2^n - 2^j$ for any positive integer $n$, some non-negative $j$. But how do I prove this using induction?
Thanks,