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Math Help - Elementary # Theory

  1. #1
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    Elementary # Theory

    Hey guys, i got a midterm coming this thursday, n really try to crack it asap.

    thanks very much for you guys' help.

    Show that the sum of twin primes p & p+2 is divisible by 12, provided that p is greater than 3.
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  2. #2
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    Quote Originally Posted by felixmcgrady View Post
    Hey guys, i got a midterm coming this thursday, n really try to crack it asap.

    thanks very much for you guys' help.

    Show that the sum of twin primes p & p+2 is divisible by 12, provided that p is greater than 3.
    primes greater than 3 can only be congruent to 1, 5, 7 and 11 modulo 12, so if p and p+2 are twin prines p is congruent to 5 and p+2 to 7, or p is congrurnt to 11 and p+2 to 1.

    case 1: for some natural number n; p+(p+2)=12n+5+12n+7=24n+12 so the sum is divisible by 12.

    case 2: for some natural number n; p+(p+2)=(12n+11)+(12(n+1)+1)=24n+24, so the sum is divisible by 12.

    RonL
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