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