Hello, smithhall!

I don't have rigorous proofs for my claims.

(a) Determine which positive integers have exactly 3 positive divisors

and prove your statement.

Suppose is the product of two distinct primes: .

. . Then hasdivisors: .four

To have exactly 3 divisors, the two prime factors must be equal: .

. . The divisors are: .

Therefore,Nmust be the square of a prime.

(b) Determine which positive integers have exactly 4 positive divisors

and prove your statement.

We answered this question in part (a).

must be the product of exactly two distinct primes.