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Math Help - Twin Primes Problem

  1. #1
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    Twin Primes Problem

    Prime numbers x and y are called twin primes, if y = x + 2. Prove that the numbers x^4 + 4 and y^4 + 4 are never relatively prime, if x and y are twin primes?

    I'm not sure how to correctly approach this problem, but I've tried a few things and I think that mod 4 is involved somehow.

    Please help, BG.
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  2. #2
    Super Member PaulRS's Avatar
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    Try modulo 5. - remember to check the cases that involve 5 (as one of the primes) separately-
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  3. #3
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    The approach I use:
    (and I'm guessing that you've done this.)

    y^4 + 4 Eqn1

    y = x + 2 Eqn2

    y^4 + 4 = (x+2)^4 + 4 Eqn3

    Expand the RHS and notice the difference between Eqn1 and Eqn3
    I do not know if there is a "correct" approach.
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