IMO Shortlist 2000 problem A7
Kvaliteta:
Avg: 0,0Težina:
Avg: 9,0 For a polynomial
of degree 2000 with distinct real coefficients let
be the set of all polynomials that can be produced from
by permutation of its coefficients. A polynomial
will be called
-independent if
and we can get from any
a polynomial
such that
by interchanging at most one pair of coefficients of
Find all integers
for which
-independent polynomials exist.
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
![M(P)](/media/m/1/9/5/1950c5725ae0ddcb428f73593d529156.png)
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![P(n) = 0](/media/m/9/e/1/9e1f8a4f0db4743dc5b4eda41823f241.png)
![Q \in M(P)](/media/m/9/3/e/93e85ae57f38f071dc8fc4975defad59.png)
![Q_1](/media/m/0/3/1/0313e7ec2e52d7e7514e810cd41daf66.png)
![Q_1(n) = 0](/media/m/8/3/2/832f49174fedf3ffc3260086637126fa.png)
![Q.](/media/m/7/8/b/78b8b2b44099003e844b852726990bc5.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
Izvor: Međunarodna matematička olimpijada, shortlist 2000