Multiplication of primitive roots

[trisacloon]

Hi

I noticed that multiplication of all primitive roots modulo p ,p>3,
congruent to 1 modulo p...

I have tried some examples (13,17,19...) but i couldn't prove the general case
(let g1...gk be primitive roots modulo p,p>3 ==> g1*g2*...*gk=1(p))

I need help to prove or disprove it...

thanks in advance

 

[Hurkyl]

Hi

I noticed that multiplication of all primitive roots modulo p ,p>3,
congruent to 1 modulo p...

I have tried some examples (13,17,19...) but i couldn't prove the general case
(let g1...gk be primitive roots modulo p,p>3 ==> g1*g2*...*gk=1(p))

I need help to prove or disprove it...

thanks in advance

Try multiplying them in a clever order.

 

[trisacloon]

thanks for the replay
I'll try to follow your lead ...

 

[robert Ihnot]

I would suggest looking at detail, leave no stone unturned!

 

[trisacloon]

I will rephrase my question...
How can i explain that if g is a primitive root then g^-1 is primitive root?

 

[Hurkyl]

I will rephrase my question...
How can i explain that if g is a primitive root then g^-1 is primitive root?

I would have expected it to be straightforward, although I haven't worked it out explicitly.

Where, when proving the inverse of a primitive root is primitive, do you get stuck?

 

[matt grime]

It's a group. The order x and x^-1 are trivially shown to be the same.

 

[robert Ihnot]

If 1/g^k ==1, Mod M, then of course, g^k==1 Mod M.