suppose p denotes a prime congruent to 3 modulo 4; use wilson's theorem to prove that

Question

suppose p denotes a prime congruent to 3 modulo 4; use wilson's theorem to prove that

 

(P-1/2)!²   ≡ 1 (mod p)

 

 Hint: Prove that  ((p-1)/2)!²  ≡  (p-1)!  (mod p)

 

 

 

 

Please explain the thinking process behind the proof and show all work. Thanks so much for your help!!

Answer 1

Jessia,

 

I do not like to be reproaching, but in a number theory class, it is not advisable to ask for help with proofs. This is one of those math classes in which every student must struggle on their own to find their own way of solving a problem.

 

I recommend you read about Wilson's Theorem in your textbook and try to think about this on your own. It is not helpful to have someone tutor you in a subject which requires more advanced help than we usually provide in this format. I may be overstepping my authority, but most of the questions asked here are at the level of basic college math or below. I could help you, but I do not think you would benefit from it.

 

You might also consult with a fellow student or ask your professor for some help with this if you continue to get stuck.

 

Sorry.