How many polynomials are there, which satisfy all the following conditions:
Details and assumptions
A polynomial is monic if its leading coefficient is 1. For example, the polynomial is monic but the polynomial is not.
As stated in the problem, the coefficients are real values, not necessarily integer valued.
Clarification: The divisibility condition in 4 is about polynomials, not integer values obtained upon evaluation. For example, divides . since . does not divide , even though when "", 1 divides 8.