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prime cube

Posted on: February 22nd, 2014 by
3

7 is a prime number and 7+1=8 is a perfect cube. Can you find another prime number p such that p+1 is a perfect cube?

- via Daily Brain Teaser


3 Responses to prime cube

  1. Lizard had this to say about that:

    No because x^3 - 1 = (x - 1)(x^2 + x + 1), which is clearly not prime if x > 2.

    • Sid Hollander had this to say about that:

      When x = 2 is the ONLy time you get a prime. i.e 7.

      Assume the integer c cubed follows prime P then
      Then c^3 -1 = P
      But c^3 -1= (c-1)(c^2 + c + 1)
      The right side is composite unless (c-1) = 1
      (c-1) = 1 iff c=2
      If c=2 then (c^2 + c + 1) can only =7

      • Sid Hollander had this to say about that:

        Wh do you correct/edit the reply that Lizard gave and not edit mine?

        Grow up phd candidate.


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