Let n be any positive integer, and let pn denote the smallest prime number that evenly divides n. Prove that there are infinite number of integers n such that pn ≥ √ n. (This fact establishes that we...

Let n be any positive integer, and let pn denote the smallest prime number that evenly divides n. Prove that there are infinite number of integers n such that pn ≥ √ n. (This fact establishes that we cannot change the bound in the aforementioned theorem to anything smaller than √ n.)