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Math Help - Prime factor problem

  1. #1
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    Prime factor problem

    Prove that each integer of the form 3n+2 has a prime factor of this form.

    proof. Let a = 3n+2, suppose that p | a, p prime, then px = 3n + 2

    Then I'm stuck, or should I write p = 3q + r?
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Prove that each integer of the form 3n+2 has a prime factor of this form.

    proof. Let a = 3n+2, suppose that p | a, p prime, then px = 3n + 2

    Then I'm stuck, or should I write p = 3q + r?
    Assume not. Then its prime factors p1,...,pn all have the form 3k+1. But then p1*p2*...*pn has the form 3k+1 also which is a contradiction.
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