Question

prove that any prime of the form 3k + 1 is of the form 6k +1.

Answer 1

Let k = 2m. Then a prime of the form 3k + 1 is of the form 3(2m) = 1 = 6m+1. Prove that any positive integer of the form 4k + 3 must have a prime factor of the same form. ... Proof: Since a number of the form 6k + 5 is odd and not divisible by 3 it can't have any factors of the form 6k, 6k + 2, 6k + 3, or 6k + 4.