Prove that any prime of the form 3m 1 for some is also of t

Prove that any prime of the form 3m + 1 for some is also of the form 6n + 1 for some n N.

Solution

all primes except 2 are odd and for no integer m,we can represent 2 as 3m+1. so the given prime 3m+1 must be odd then 3m is even then m must be even as only even multiplied by odd gives even let m=2*n where n=any integer then the given prime=3m+1=6n+1 for some integer n (proved)