The question is :
What positive integers has exactly (and prove your result) (a) one positive divisor; (b) two positive divisors; (c) three positive divisors; (d) four positive divisors; (e) five positive divisors.
I think that,
for (a), the answer should be only integer 1.
for (b), that answer should be all the primes
for (c), that answer should be all the integer a satisfy a = prime^2
(d) and (e) should be similar but I am not sure.
My confusion is about how to prove these five cases. Any hints or sample prove for part (c) will be pretty helpful.