(a) Determine which positive integers have exactly 3 positive divisors and prove your statement.
(b) Determine which positive integers have exactly 4 positive divisors and prove your statement.
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 has four divisors: .
To have exactly 3 divisors, the two prime factors must be equal: .
. . The divisors are: .
Therefore, N must 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.