Problem #1792
Back to Complex Numbers page
1792.

Let be the set of polynomials of the form
where are integers and has distinct roots of the form with and integers. How many polynomials are in ?
This problem is copyrighted by the American Mathematics Competitions.

Note: you aren't logged in. If you log in, we'll keep a record of which problems you've solved.
Instructions for entering answers:
 Reduce fractions to
lowest terms and enter in the form 7/9.
 Numbers involving pi should be written as 7pi or 7pi/3
as appropriate.
 Square roots should be written as sqrt(3),
5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
 Exponents should be entered in the form 10^10.
 If the problem is multiple choice, enter the appropriate
(capital) letter.
 Enter points with parentheses, like so: (4,5)
 Complex numbers should be entered in rectangular form
unless otherwise specified, like so: 3+4i. If there is no
real component, enter only the imaginary component (i.e. 2i,
NOT 0+2i).
For questions or comments, please email markan@eudelic.com.