Question

Show that if the smallest prime factor p of the positive integer n is larger than n^(1/3), then n/p is prime or equal to 1.

Answer 1

To show that if the smallest prime factor p of the positive integer n is larger than n^(1/3), we need to consider two cases: If n/p is prime, then the statement is true because we have a prime factorization of n. If n/p is equal to 1, then the statement is also true because it implies that p is equal to n, which is a prime number.

Step-by-step explanation:

To show that if the smallest prime factor p of the positive integer n is larger than n^(1/3), we need to consider two cases:

1. If n/p is prime, then the statement is true because we have a prime factorization of n.
2. If n/p is equal to 1, then the statement is also true because it implies that p is equal to n, which is a prime number.

Hence, if the smallest prime factor p of n is larger than n^(1/3), then n/p is either prime or equal to 1.