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Here is the complete proof taken from this link

enter image description here

How do I convince myself that n(1+b) is not prime when b>=1? Here is what I did: if n is 3 and b is 3. Then resulting string 111 111 is prime. Is this how it should be done it in proofs? The way I see is this. If n(1+b) is not proved for even one set of values then I can say it is not prime. Set of values in this case was n =3 & b = 3.

Is this approach of understanding poofs is right?

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The number $n(1+b)$ is not prime because it has 2 divisors greater than 1. These are $(b+1)$ and $n$. I believe that's what is meant here.

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  • $\begingroup$ If there is only one state in DFA then because of n>=p, n can be equal to 1. What happens then? Now at least one of factor is 1. @peter.petrov $\endgroup$ – user3461957 Jun 9 '15 at 14:43
  • $\begingroup$ It says n is prime number. So n cannot be 1. $\endgroup$ – peter.petrov Jun 9 '15 at 19:45

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