Question 48
Let us say that an integer number is a power number, if there exist positive integers $a$ and $n$ such that the number equals to $a^n$ and $n \gt 1$.
a) Prove that there exist $2010$ positive integers such that every sum of the integers selected from them is not a power number.
b) Prove that there exist $2010$ positive integers such that every sum of the integers selected from them is a power number.
a) Prove that there exist $2010$ positive integers such that every sum of the integers selected from them is not a power number.
b) Prove that there exist $2010$ positive integers such that every sum of the integers selected from them is a power number.