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Math Help - Finding all primes P

  1. #1
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    Post Finding all primes P

    Can someone help me with how to go about this problem?

    Find all primes p such that:

    8p^2 + 1 is also a prime,

    Thanks

    -Kate
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  2. #2
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    Quote Originally Posted by katie07 View Post
    Can someone help me with how to go about this problem?

    Find all primes p such that:

    8p^2 + 1 is also a prime,

    Thanks

    -Kate
    If p is odd then p = 1(mod 3) or p = 2(mod 3) in either case p^2=1(mod 3) so 8p^2+1 is always divisible by 3.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    If p is odd then p = 1(mod 3) or p = 2(mod 3) in either case p^2=1(mod 3) so 8p^2+1 is always divisible by 3.

    So you leave the possibilities p=2 or p=3.

    Now for p=2

    8p^2+1 = 33

    which is not prime.

    For p=3

    8p^2+1 = 73

    which is prime.

    RonL
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