# 1000 degree polynomial

• Apr 11th 2013, 06:24 PM
geniusgarvil
1000 degree polynomial
How many polynomials f(x) are there, which satisfy all the following conditions:
1. f(x) is monic.
2. f(x) has degree 1000.
3. f(x) has real coefficients.
4. f(x) divides (x1)f(2x).
5. f(2) is an integer.