# Mod proof with primes

• Jan 30th 2010, 05:37 PM
Mod proof with primes
If p is greater than or equal to 5 and p is prime, prove that [p]=[1] or [p]=[5] in Z6.

I think that we will have to consider cases, that is,

p=6q, p=6q+1, p=6q+2, p=6q+3, p=6q+4, p=6q+5....

Since p is prime, we have p divides p and 1 divides p....Also, since p is greater than or equal to 5, it must be odd, i.e. like 2k+1, but I don't know if this is useful.

I really don't know what I need to show this....
• Jan 30th 2010, 06:10 PM
tonio
Quote:

If p is greater than or equal to 5 and p is prime, prove that [p]=[1] or [p]=[5] in Z6.

I think that we will have to consider cases, that is,

p=6q, p=6q+1, p=6q+2, p=6q+3, p=6q+4, p=6q+5....

Since p is prime, we have p divides p and 1 divides p....Also, since p is greater than or equal to 5, it must be odd, i.e. like 2k+1, but I don't know if this is useful.

I really don't know what I need to show this....

If \$\displaystyle [p]=0,2,4\!\!\!\pmod 6\$ then p is even, if...etc.

Tonio
• Feb 1st 2010, 06:32 PM
Deepu
Quote: