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Math Help - number theory, prime

  1. #1
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    number theory, prime

    Find the smallest prime in the arithmetic progression an + b , where
    a) a = 5, b = 1
    b) a = 7, b = 2
    c) a = 23, b =13


    Thanks very much guys!!!
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  2. #2
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    Quote Originally Posted by suedenation View Post
    Find the smallest prime in the arithmetic progression an + b , where
    a) a = 5, b = 1
    b) a = 7, b = 2
    c) a = 23, b =13


    Thanks very much guys!!!
    Just list your number out until you reach a prime (by Dirichelts theorem there will be primes in fact infinitely many).
    ---
    a)5n+1:
    6,11,--->We got a prime.

    b)7n+2:
    9,16,23,--->We got a prime.

    c)23n+13:
    36,59,--->We got a prime.
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