Is there something faulty about this statement? Show any prime of the form $3k+1$ is of the form $6k+1$. 
I came up with my own solution that made perfect sense to me, but when I read the text's solution, it argued that for the primes that are of the particular form are $6k+1 = 3(2k)+1$. But doesn't that really say the primes in the form of $3k+1$ are in the form of $6m+1$? It seems to me as though there's some misuse of notation here -- allowing $k = 2k$. So should the exercise be phrased as $6m+1$ instead? 

Another way to phrase it is
"If k is a positive integer such that 3k+1 is prime
then k is even".
The proof, of course, is easy:
If k is odd, then k=2h+1 for some integer h.
But 3k+1 = 3(2h+1)+1 = 6h+4 is even
and therefore not prime.
