MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
BMT Problems
2013 BMT Spring
5
BMT 2013 Spring - Discrete 5
BMT 2013 Spring - Discrete 5
Source:
January 6, 2022
algebra
Polynomials
Problem Statement
Consider the roots of the polynomial
x
2013
−
2
2013
=
0
x^{2013}-2^{2013}=0
x
2013
−
2
2013
=
0
. Some of these roots also satisfy
x
k
−
2
k
=
0
x^k-2^k=0
x
k
−
2
k
=
0
, for some integer
k
<
2013
k<2013
k
<
2013
. What is the product of this subset of roots?
Back to Problems
View on AoPS