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? 

The only $k$ for which $3k+1=6k+1$ is $k=0$, which doesn't even give a prime. The statement means "if a prime is a multiple of three plus one, then it is a multiple of six plus one". The $k$ is a dummy variable; although it is not proper to us $k$ twice, the statement is not much clear if you use two different variables. 
