2021 JMC 10 Problems/Problem 22
Problem
Let be the roots of
Suppose
is the monic polynomial with all six roots in the form
for integers
What is the coefficient of the
term in the polynomial
Solution
Note that has
terms. We can also see that all terms are in the form
or
. The only way
are produced is
and there are
pairs of these for a given value of
.
So three copies of each is produced, and there are
copies of
by symmetry. By Vieta's, our desired answer is equal to