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Thread: Prime # Proof

  1. Apr 21st 2010, 05:43 PM #1
    MATNTRNG
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    Prime # Proof

    Let a, b, c, and d be natural numbers. Show that if ab = cd, then a² + b² + c² + d² is not prime. Generalize.
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  2. Apr 21st 2010, 06:06 PM #2
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    Quote Originally Posted by MATNTRNG View Post
    Let a, b, c, and d be natural numbers. Show that if ab = cd, then a² + b² + c² + d² is not prime. Generalize.
    I think the start goes like this:

    a^2+b^2+c^2+d^2

    =a^2+2ab+b^2+c^2-2cd+d^2

    =(a+b)^2+(c-d)^2
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