SOLUTION: Any prime number greater then 3 can be written in the form of 3k+1 or 3k-1?

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Question 1144789: Any prime number greater then 3 can be written in the form of 3k+1 or 3k-1?
Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
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Any prime number greater highlight%28cross%28then%29%29 than 3 can be written in the form of 3k+1 or 3k-1?
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Yes, it is a correct statement.

It is because any prime number greater than 3 gives the remainder 1 or 2 when is divided by 3

(simply because such a prime number is not multiple of 3).

If it gives the remainder of 1, then it is of the form 3k+1.

If it gives the remainder of 2, then it is of the form 3k-1. 

          Keep in mind that the reverse statement is not true - 

             not every integer of the form 3k+1 or 3k-1 is a prime    (!)