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Let $m$ be a positive integer such that $m$ has exactly 5 positive divisors. How many distinct prime factors does $m$ have

Respuesta :

If m has exactly 5 positive divisors then there can only be one prime factor.

According to statement

m has exactly 5 positive divisors AND

Let A^p,B^q,.... are the possible factors of integer m then

assume that p and q ≥ 1.

then the number of possible divisors cannot be 5 because there are no two integers  p, q ≥ 1, such that (p +1)(q + 1) = 5

So, If m has exactly 5 positive divisors then there can only be one prime factor.

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