Mock AIME 3 2006-2007 Problems/Problem 3
Problem
Let . If
is a polynomial whose roots are the 59th powers of the roots of
, then find the sum of the roots of
.
Solution
Let denote the roots of P. Then,
. Therefore,
.
Denote. So
. To find
, use Newton's recursive sums:
.
Solving, we get .