Question 16
An integer $m$ is a genuine power if there are positive integers $a,n$ with $n\gt 1$ and $m=a^n$.
a. Prove that there exist $2012$ distinct positive integers such that no nonempty subset has a sum that is a genuine power.
b. Prove that there exist $2012$ distinct positive integers such that every nonempty subset has a sum that is a genuine power.
a. Prove that there exist $2012$ distinct positive integers such that no nonempty subset has a sum that is a genuine power.
b. Prove that there exist $2012$ distinct positive integers such that every nonempty subset has a sum that is a genuine power.