Question 64
Let $(a_n)_{n\in\mathbb N}$ be a nondecreasing, nonconstant sequence of positive integers such that $a_n$ divides $n^2$ for every n≥1. Prove that one of the following holds:
a) There is an integer $n_1\gt 0$ such that $a_n=n$ for every $n\ge n_1$.
b) There is an integer $n_2\gt 0$ such that $a_n=n^2$ for every $n\ge n_2$.
a) There is an integer $n_1\gt 0$ such that $a_n=n$ for every $n\ge n_1$.
b) There is an integer $n_2\gt 0$ such that $a_n=n^2$ for every $n\ge n_2$.