Recent content by S_Manifesto

None of what I have read has made sense...

Show that every finite field with p+1 elements, where p is a prime number, is commutative. I know this has something to do with composite numbers, but I'm not quite sure how to show this.

The question has a plus with a circle around it, I don't know how to make that symbol. But that's correct?

What I came up with was (x*y)=(y*x) → x+y+2 = y+x+2 to show it's albein. x+(y+z)=(x+y)+z → x+(2yz+4y+4z+6)=(2xy+4x+4y+6)+z and got 4xyz+8xy+8xz+8yz+16x+16y+16z+30 = 4xyz+8xy+8xz+8yz+16x+16y+16z+30 For x+(y*z)=(x+y)*(x+z) → x+(y+z+2)=(2xy+4x+4y+6)*(2xz+4x+4z+6) and got 2xy+2xz+8x+4y+4z+14 =...

1) Show that (R,*,+) is a ring, where (x*y)=x+y+2 and (x+y)=2xy+4x+4y+6. Find the set of unit elements for the second operation. I understand that the Ring Axioms is 1. (R,+) is an albein group. 2. Multiplication is associative and 3. Multiplication distributes. I just don't understand how to...