Prove that any prime p > 3 is either of the form 6k + 1 or of the form 6k + 5 for some integer k.

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

By the division algorithm, any integer can be written in one of the forms 6k, 6k + 1, 6k + 2, 6k + 3, 6k + 4, 6k + 5.

Of these, 6k, 6k + 2 and 6k + 4 are even, and 6k +3 is divisible by 3.

Thus, none of these can represent a prime > 3.

Thus p must be of the form 6k + 1 or 6k + 5.