Can the positive integer k be expressed as the product of two integers, each of which is greater than 1?
(1) k^2 has one more positive factor than k.
(2) 11 < k < 19
I don't understand well this explanation of the OE. Please, your help:
The only types of numbers k such that k2 has exactly one more positive factor than k are primes. Prime numbers have two factors and their squares have three. If k had more than two factors, the number of factors would increase by more than 1 when squared. Thus, k must be prime, answering the question.
(1) k^2 has one more positive factor than k.
(2) 11 < k < 19
I don't understand well this explanation of the OE. Please, your help:
The only types of numbers k such that k2 has exactly one more positive factor than k are primes. Prime numbers have two factors and their squares have three. If k had more than two factors, the number of factors would increase by more than 1 when squared. Thus, k must be prime, answering the question.
