2020 AIME II Problems/Problem 3
Problem
The value of that satisfies
can be written as
, where
and
are relatively prime positive integers. Find
.
Solution
Let . Based on the equation, we get
and
. Expanding the second equation, we get
. Substituting the first equation in, we get
, so
. Taking the 100th root, we get
. Therefore,
, so
and the answer is
.
~rayfish