Hi there (again),

I tried going about a proof to the following proposition,

Any symmetric integral polynomial in

is a symmetric polynomial in

,

and it was this

Let us denote our symmetric integral polynomial by

Then, we know that there exists some polynomial g that satisfies the relation

We conclude that g is also a symmetric integral polynomial, since the zeros are not labelled, and so are unaffected by any permutation

on the set

Now, this is wrong. I have to admit, it was a total stab at a proof. Does anyone know why this is wrong, and how would you go about doing this?

EDIT: Of course, all of are integers