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Math Help - find entier number n and p

  1. #1
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    find entier number n and p

    plz find entier numbers n and p which make the following system to have solutions

    z^n=1
    (1+z)^p=1

    plz help
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  2. #2
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    Quote Originally Posted by saucisson View Post
    plz find entier numbers n and p which make the following system to have solutions

    z^n=1
    (1+z)^p=1
    Those equations imply that both z and 1+z lie on the unit circle. The only such points are z = -\tfrac12\pm\tfrac{\sqrt3}2i, so that n=3 and p=6 (or multiples thereof).
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  3. #3
    MHF Contributor chisigma's Avatar
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    Under the hypothesis that 0 \in \mathbb {Z}, z=0, n=0 and p \in \mathbb{Z} arbitrary is also solution...

    Kind regards

    \chi \sigma
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