Show How p Equals 1 or 5 in Z_6 (mod 6)

[Pearce_09]

Hello,
I am just going to post question i have tried it yet.. only because i don't understand the question.. so if you could help me read the question that would be good.. and if you want to give a hint feel free..

If p does not equal 2, 3 is prime, show that p = 1 or p = 5 in $$Z_6$$ (mod 6)

ok what i don't understand is.. is the question saying that p does not also equal 3.. or is it just telling me that 3 is a prime.. cause that obvious..
or is it saying p does not equal 3 but its prime.. I am not sure.. so i can't really go any further.. thank you

 

[benorin]

I think it would mean that p is a prime other than 2 or 3.

 

[benorin]

this seems ok (this is not a proof by any means,) but for p=5,7,11,13,17,19,23,29,31 it works. so It seems that our interpetation of the hypothesis on p is correct.

 

[Pearce_09]

awsome..thats what i was thinking to.. thanks!

 

[matt grime]

The question just means "if p is a prime not equal to 2 or 3". Exactly what it says. It says nothing about what 2 or 3 are at all, primes or not.

If we were to remove the requirement that p not be 2 or 3 then the statement would read: suppose p is a prime, show p is congruent to 1 or 5 mod 6. And that would be false since there are two primes that are not congruent to 1 or 5 mod 6. However all primes except 2 and 3 are congruent to 1 or 5 mod 6. now let's prove it...

I don't see why this meant you couldn't go further. the question was specifically not about the primes 2 or 3.