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Math Help - finding primes

  1. #1
    Junior Member mathbuoy's Avatar
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    Unhappy finding primes

    How many primes are in the form 4n^8+1, where n is a positive integer?

    *show working n explanation, PLS...
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  2. #2
    MHF Contributor
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    Hello
    n=5p (where p is an integer) is a necessary condition but I do not know if it is a sufficient condition

    If n=5p+1
    Then n^8=(5p+1)^8=5P+1
    Therefore 4n^8+1=20P+5 is divisible by 5 => not prime

    If n=5p+2
    Then n^8=(5p+2)^8=5P+2^8=5P+256
    Therefore 4n^8+1=20P+1025 is divisible by 5 => not prime

    If n=5p+3
    Then n^8=(5p+3)^8=5P+3^8=5P+6561
    Therefore 4n^8+1=20P+26245 is divisible by 5 => not prime

    If n=5p+4
    Then n^8=(5p+4)^8=5P+4^8=5P+65536
    Therefore 4n^8+1=20P+262145 is divisible by 5 => not prime
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