Question 74
Let $A = \{1, 3, 3^2, 3^3, \dots, 3^{2014}\}$. We obtain a *partition* of $A$ if $A$ is written as a disjoint union of nonempty subsets.
a) Prove that there is no partition of $A$ such that the product of elements in each subset is a square.
b) Prove that there exists a partition of $A$ such that the sum of elements in each subset is a square.
a) Prove that there is no partition of $A$ such that the product of elements in each subset is a square.
b) Prove that there exists a partition of $A$ such that the sum of elements in each subset is a square.