# Question about symmetric integral polynomials

I read a proof of the transcendence of $$pi$$ but I'm stuck with a problem about polynomials. The proof begins like this:

"Suppose $${ beta _1}, { beta _2}, ldots, { beta _n}$$ are the roots of an equation

$$d {x ^ m} + {d_1} {x ^ {m – 1}} + ldots + {d_m} = 0$$

with integral coefficients. Any symmetrical integral polynomial in

$${d beta _1}, {d beta _2}, dots, {d beta _n}$$

is an integer. "

Can any one explain it please?