a special polynomial

[alinbostan]

Let n > 1 be a positive integer, let E={+1,-1}^n, let s=(s_1,...,s_n) in E,
let f_s:=s_1 sqrt(x+1)+...+s_n sqrt(x+n) and let N(x)=prod_{s in E} f_s.

Prove that N(x) is a polynomial in Z[x] and determine its degree in x.

Good luck !

_________________
The Owls Are Not What They Seem

[Valentin Vornicu]

is this an open question, or a own questions to which you have the answer to?

[alinbostan]

> is this an open question, or a own questions to which you have the answer to?

I have a partial answer to this question. I did not post it to the
"Unsolved Problems" section, because I do not consider that it matches
the definition "Problem you couldn't solve and to which you know that
there is a solution (i.e. a problem from a contest, etc.) but you
don't know it". I had the same doubt while thinking to send it to the "Proposed & Own
Problem" section, whose definition is "Problems that you have already
solved and you are interested in second opinions or solutions"...
By the way, what exactly your definition of an "open question" is ?

Alin.

[Valentin Vornicu]

an open question is obvioulsy a question that is not closed

however a more detalied description could be the following:

An open question is a question that has no known solution up to this moment, and it is not known wheter the problem has one or not.

[alinbostan]

I see. Maybe you should put down this definition at
http://www.artofproblemsolving.com/Forum/viewforum.php?f=3
as you did for the other themes.

_________________
The Owls Are Not What They Seem