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Math Help - Prime

  1. #1
    Junior Member
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    Prime

    Hi everybody

    (a,b)\in \mathbb{Z}^2, p is prime number,

    I must show that p/(a^2+b^2) and p/(a^2b^2)\Longrightarrow p/a and p/b

    How to do it?
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  2. #2
    Banned
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    Quote Originally Posted by lehder View Post
    Hi everybody

    (a,b)\in \mathbb{Z}^2, p is prime number,

    I must show that p/(a^2+b^2) and p/(a^2b^2)\Longrightarrow p/a and p/b

    How to do it?
    p\mid a^2b^2\Longrightarrow p\mid a\,\,\,or\,\,\,p\mid b , since p is a prime. Suppose p\mid a and thus also p\mid a^2\Longrightarrow p\mid(a^2+b^2)-a^2\Longrightarrow p\mid b^2\Longrightarrow p\mid b as well.

    Tonio
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