Loading ...
Sorry, an error occurred while loading the content.

RE Has this been proven??

Expand Messages
  • Jose Ramón Brox
    ... From: newjack56 Does anyone know if this has been proven? Given any prime p, p is congruent to 1 (mod 2) If this has been proven,
    Message 1 of 1 , Feb 2, 2006
    • 0 Attachment
      ----- Original Message -----
      From: "newjack56" <mrnspealum@...>


      Does anyone know if this has been proven?

      Given any prime p, p is congruent to 1 (mod 2)

      If this has been proven, what are some conjectures (I believe) that
      haven't been proven yet?

      ----------------------------------------------

      Hi:

      Are you serious??? I fear you are!

      Let's see: first of all, defined in such way it is FALSE:

      p=2 is a prime, and 2 = 0 (mod 2).

      And if you say that given any prime p>2, then p = 1 (mod 2), it's trivially TRUE, because:

      p = 1 (mod 2) means that p IS NOT a multiple of 2.
      Any prime bigger than 2 CANNOT be a multiple of 2, because otherwise it would be a
      composite.
      Therefore, p>2 --> p = 1 (mod 2)

      You can extend it to say that any p>3 can't be p=0 (mod 3), any p>5 can't be p=0 (mod
      5)... and so on.

      Jose Brox
    Your message has been successfully submitted and would be delivered to recipients shortly.