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Math Help - Prime or not?

  1. #1
    Junior Member
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    Canada Ontario
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    Prime or not?

    hi,
    Is the following statement wrong?
    If C(p-1,(p-1)/2) mod p = p-1 then p is prime
    Exemple :
    p=7
    C(6,3)=20
    C(6,3) mod 7 = 6
    If it is correct how can we prove it?
    Thank you very much for any comment.
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  2. #2
    Junior Member
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    Re: Prime or not?

    Any counterexample?
    5 is prime C(4,2) mod 5=1

    My claim is that if C(p-1,(p-1/2)) mod p= p-1 THEN p is prime.
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  3. #3
    Junior Member
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    Re: Prime or not?

    The fisrt counterexample was found.
    p=5097 is composite
    I do not know if there are other counterexamples.
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