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Math Help - Question #1: Prime

  1. #1
    Mel
    Mel is offline
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    Question #1: Prime

    If p is an odd prime, show that p is of the form.

    (a) 4n + 1 or 4n+3 for some n.

    (b) 6n + 1 or 6n + 5 for some n.
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  2. #2
    MHF Contributor
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    (a) is straightforward. If p is odd, then it cannot be a multiple of 2, which rules out 4n and 4n + 2. Then p must be either 4n + 1 or 4n + 3.

    (b) is a little harder but not much. If p is odd, then it is either 6n + 1, 6n + 3, or 6n + 5. However, 6n + 3 = 3(2n + 1) and is not prime. Therefore, p is either 6n + 1 or 6n + 5.
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