Final answer:
To show that if n is a positive integer such that the sum of its positive divisors is n+1, then n is prime, use proof by contradiction. Assume that n is not prime and can be factored into two positive integers, a and b. Then calculate the sum of the positive divisors of n, which is greater than n, contradicting the assumption. Therefore, n must be prime.
Step-by-step explanation:
To show that if n is a positive integer such that the sum of its positive divisors is n+1, then n is prime, we can use proof by contradiction.
Assume that n is not prime, which means it can be factored into two positive integers, a and b, where a > 1 and b > 1. Then we can write n = a * b.
But if n = a * b, then the sum of the positive divisors of n can be calculated as (1 + a + b + a * b), which is greater than n.
This contradicts the assumption that the sum of the positive divisors of n is n+1. Therefore, our assumption that n is not prime must be false, and we can conclude that n must be prime.