Prove infinitely many prime of the form 6k+5

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Homework Statement


Prove that there are infinitely many prime of the form 6k+5, where k is nonnegative integer.


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The Attempt at a Solution


Prove by contradiction. Suppose there are finitely many prime of the form 6k+5. Then
i get stucked. Anyone can help me ??
 
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Well, there isa result that any arithmetic progression an=a0+nr
with a0 and r relatively prime contains infinitely-many primes. Is that the type of proof you want (adapted to a0=5 and r=6)?
 
You got "stucked" before you really got started. Suppose M=p1*p2*...*pk where the p's are your primes. Think about the prime factorization of 3*M+2. Can you show none of the p's are factors? Can you show at least one of the factors must be equal to 5 mod 6?
 
Bacle2 said:
Well, there isa result that any arithmetic progression an=a0+nr
with a0 and r relatively prime contains infinitely-many primes. Is that the type of proof you want (adapted to a0=5 and r=6)?

That proof is way too hard. There are simpler proofs for special cases. This is one of them.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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