... 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,

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, Feb 2, 2006

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----- 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?

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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

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